Mastering Quantitative Techniques for CAT

1 by 7 multiplied by 5 by 9 into 63 is equals to 5. Arey, aap log aage? Welcome to your pyarasa channel MBA wala. Welcome to your batch CAD essentials. Welcome to a revolution. Kis cheech ka revolution? Chalaiya jaante. Toh for all CAD 2024 experience. Guys, first of all, this is Rahul Bhatla, your quant faculty from MBA wala channel. Now we will start a revolution here. We will teach you essential things which are necessary to start your CAT journey. Otherwise, many times they make you lose a little bit of confidence in between. If you don't know the basic things, sometimes they off track you from your journey. You start getting scared. Why? Because you have competition with students from all over India who are aiming for CAT or CAT exam, IIMs or good business schools. Now what happens is that, Here you will find some people who are extraordinary better than you. Right. Some people who are like you. Some people who are a little weaker than you. So if you are a student from average mathematical background or below average mathematical background, then what happens is that we do not understand some basic things. It comes out of our mind. Or we get concepts, but we are not able to apply those tricks. And some children who are actually good in quant, good in mathematics, they forget that this is not a math exam, it is an aptitude exam. Right? You study well, after 8 months you learn concepts, then what happens is that when you go for mock tests or you go for sample questions, the questions are being made, there is no problem. But in those 40 minutes, you are able to do only 9 or 8 or 10 out of 22 questions. And because of that, your score does not come. And then you keep thinking that how are they doing the questions that their question is so fast that they are able to make it up to. 14 or 15 questions. Whereas, ours are only 8 or 10. And the difference is in the percentile. Whereas, when we get all the math, then we start looking for the problem. The problem is guys, approaches. So, this CAT Essential Series, the upcoming series, which is going to target 100 percentile for you, is the base, is the foundation, which will help you know that what are the approaches, which we use in CAT Quant. What are the aptitudes we apply in CAT Quant? You will know today that this is not a maths exam, this is a quant aptitude exam and there are approaches which will make the questions look easier and by which you can do the questions within 30 seconds, 40 seconds. The questions which look very big. For instance, I will give you one more example. This was a simple, right straight forward equation. Let us see a problem solving question. This type of question. Invest at the left. Now, after reading all these questions, it takes us at least 1-2 minutes. Because we are following standard mathematics, we are accepting x, we are accepting everything, we are accepting y, we are making z equations. But after today's class, how are you going to do this question? Do you want to see? Look guys, I am going to learn this question. Now, whether you understand or not, it doesn't matter. We are going to learn all this. If I were in your place, I would have done this question in such a way that I would have assumed that Mr. Rahul had 100 rupees. 30% was given to Rora sir, so out of 100, 30 was left, 70 was left. 50% remaining Vinit sir ko de diye to 35 aur chale gaya, bache 35. 35 ko invest kar diya aur wo double ho gaya, yaani ki ye ho gaya 70. Ab 100 leke aya the 70 tak poch gaya, yaani 30 niche chala gaya which is 30% decrease. Itna likh raha hai ek bacha. That is why he is able to do questions in quick time than you. And if you are following this approach, perfect. And then we have many more planted for you in this particular session. Jisko nahi samajh mein aaya, that means a lot to learn for you guys. I mean, today we are going to learn a lot. So, fasten your seat belt and let's get ready. Again, a very warm welcome to the first session of CAD Essentials. We will talk about Quant Percentage. Today we will talk about the whole thing and we will talk about the lecture number 1. Myself Rahul Batla, your Quant Faculty. Okay, let's start the game. First, we will learn the basics. I will take the tricks from the basics till the end. I will also show you some of the PYQs of some of your CAD. And by the time you go, you will also be so fast that you will be able to solve the question by assuming a good number. Remember, I will not assume 100 every time like the last question. So, till now, the talks are done. Let's start the game now. Come on, son. Topics. Percentage and ratio. How are they related? What happens? Is percentage and ratio the same thing? We will talk about all of them. How to assume a number? How to assume a number? Right? Assumption plus unitary method multiplying factor. This is the main topic of our class today. The key topics which we are going to cover are these four. Let's start the game. Here is the first game. Percent. What does it mean? Very basic. Per means something divided by. Cent means century. Hundred. It means how many out of 100 are there? For example, a child brings 10 numbers out of 20 numbers. If it continues at this rate, then how many out of 100 numbers will it bring? Sir, it's a very simple thing. This is multiplied by 5, this will also be multiplied by 5, which means 50. That means 10 by 20 is nothing but 50%. Now this is logically reached, from aptitude, but actually we will not keep taking it out like this, so how will we go? We will see that, but now what does percent mean? How many out of 100 do you bring? 10 out of 20, okay? But if it was out of 100, then how many would you bring? The thing is that you used to bring 10 out of 20, half, so you will bring half out of 100, 50, that means you have 50%. Right? Now, percent benefits us in comparing, in finding out, for example, I said one kid's number is 100, one kid's number is 200. Who scored more? You will say 200 kid did not. Which kid is good? 200 kid did not. Did you know the total marks? You did not know. So let's assume that this kid got a total of 200. And this kid got a total of 200 out of 500. Now who is more? Now it seems that the 100 number player is good. Now that's why we said that you will know if you take it out in percentage. Now to calculate the percentage, we do a simple thing. We multiply 100 on both sides. Here also multiply 100 and here also multiply 100. This will give you the percentage. Now if you solve this, it will cut 0 from 0 and 0 from 0. This will be 50. That means, the child who got 100 out of 200, this child's result is 50%. This guy is equal to nothing but 50%. Here, this is cut, this is cut, 520 goes. This child's result is 40%. Which child is good? Obviously, the child with 50% wins. And what does this mean? This means that if this child gave a paper from 100 instead of 200, then he would have got 50. Means 50% 50 per 100 Today I have come with 100, but if the paper was of 100, then he would have got 50. Similarly, he brought 200 number from 500, but if the paper was of 100, Today I have come with 200, but if it was of 100, then he would have brought 40. That means 40 Per 140%. This is the meaning of percentage. And along with that, you have also learnt to calculate the percentage. Now, you are going to get two most common statements. One is this. What is 10% of 40? Right? How do we solve them? We learn to solve them. This is the meaning. Now, what is 10% of 40? Let's understand. If I ask you, what is 10% of 40? See what you have to do. Say simple. 10. Write 10. Percent. Per. and cent, 10% off means multiply 40 means 40, this way we will get the percentage easily 0 will be deducted from 0 0 will be deducted from 0, you will get the answer as 4 Now we will get fast in some time that I will convey all this without writing the answer but first basic should be clear otherwise you will not be able to understand the tricks Once you understand the basics, then it is easy to learn the tricks otherwise you will have to keep the tricks and you will not remember the tricks for long time but if you understand then the tricks will always be with you all life long What is 20% of 30? Again, the same thing. Will you try it by pausing? I am doing it. 20 per, percent is read, so, per cent into 30. How much is it? Again, 0 to 0 is cut, 0 to 0 is cut, that is 6. What is x% of y? That means, x per cent of y. Did you understand? So, percentage sign will be removed, upon will be 100, off means multiply, y. Now, x, y, whatever happens, you will solve it. So this is the first thing we should know. Second is something like this. If you get 100 out of 200, then what is the percentage? So 10 is what percentage of 40? Simple. 10, what is the percentage of 40? So you write 10 by 40 and multiply by 100. Like 100, what is the percentage of 200? You wrote 100 by 200, you multiplied it by 200. What is the percentage of 200 by 500? You wrote 200 by 500, you multiplied it by 200. 10 by 40 is 10 by 40 into 100. How much will it be? It will be easily deducted. It will be deducted from 0 to 0. It will be 25%. So, you should know two things. One, to get the percentage. If you have 100, how much is the percentage from 500? And one, to get a percentage of any particular number. To get a percentage of any particular number. Like, what is the percentage of 40 to 10? This should be known. Only then we can move forward. Right? It is possible that you say, 20 is what percent of 50? So, 20 is 50. How much percent is there? Into 100, game over. 52 will go, you will get 40%. Similarly, x is what percent of y? So, x, y, how much percent is there? Game over. Am I clear? Once you note it down, I will move away. These two things you should definitely know. What? How to get a specific percentage of something. Second, how much is 1040%? Right, how much is 2030%? Like that we are going to do. This was a meaning story. Percent means something upon 100. How many out of 100? Percent, per 100. And the other story is this. Now let's become a little faster. Let's understand what is ratio, how percentage and ratio are related. Let's assume we have a beaker. In this beaker, 100 liters of mango juice is kept. Now a child came, he threw half a mango juice. Half a mango juice means, obviously, how much he threw? 50 liters he threw. Now see, there is one child who is telling us that you threw half a mango juice. If you... If you throw half mango juice, you have only half left, that means half is left. And one kid is saying, I am not telling you that half is left, I am telling you in percentage. He is saying, you threw 50 liters, 50 liters are left. He is saying, sir, 50 is left. From how many? From 100. How much percentage is left? 50 upon 100 into 100. You have taken out percentage like this. Something, from total, into 100. He took out this, that means 50%. Now one kid is saying, sir, 50% is left. One kid is telling in ratio that half is left. Both are right. Absolutely right. One person is telling the ratio that half is left. One child is telling the percentage that 50% is left. That means ratio and percentage are interrelated. And half is 50%. How can you see? If you simply multiply the ratio by 100, then you will get the percentage. Now if I know this, it will be very beneficial for me. Because if someone told me yesterday 50%, right? Someone told me 50% of 21. Now if I take the percentage in ratio, it will help a lot. 50% now I am doing 50% into 21. Now I can do it in my mind. 50% means half. So I am writing it straight. I am thinking about it. White line in my mind. 50% means half of 21. How much is it? 10.5. Half of 21 is left. 10.5. That's it. So sometimes your percentage will help you. You will say sir 50% would have been like this also. I would have done 50 by 100 and it would have worked. But if the question becomes like this one day. 14.28% of 777. Now one child is stuck. Why? Because he is doing this calculation. 14.28 upon 100 into 777. It worked. So aha! Now either he opens up the calculator or he is done with the question. Now, the second person who knew that the ratio of 14.28% is equal to 1 by 7. Like you knew that 50% is half. The person who knew 14.28% is 1 by 7, will do 1 by 7 into 7 is 77. He will also do this and the answer will be 1 by 1. It will be cut. That means if I know the fraction or ratio of percentage, then the question will be easy. In fact, we make the question from here. So if you solve this using a calculator, 14.28 upon 100, it will automatically come to 1 by 7, very close. 14.28 multiplied by 7 is 100. So approximately 14.28 is 7 over 100. That's how we work. Now we try to learn few percentages whose ratio is good. Like 15% becomes half. 14.28% becomes 1 by 7. How can I remember all these? Is there any trick? Let's find out. It will be very beneficial. Because yesterday I asked 14.28% of something. 14.28 is very difficult to handle. Instead of that, I will write 1 by 7. Game over. Check it. Come. I will show you some questions and I will tell you how I do it. Then I will teach you and then you do it. I would have written 25% straight. 1 by 4 into 40. This is what I am thinking. And the answer would have been 10. Now how did I write this like this? I will teach you this now. Actually what I am doing is, what do you do with 25%? 25 upon 100? And what does this become? 1 by 4? Is it true or not? I would have done this. Similarly, 33.33% I know 1 by 3. 1 by 3 of 45, I write 15 directly. Now how did you do this, sir? Son, I knew that 33.33% would become 1 by 3. Sir, how did you know? Son, when you will also see, then this 33.33 Upon 100, when you will do, 1 by 3k procs will come. I will teach you. You will also remember. But see what is the benefit of them first. 14.28%, I know it is 1 by 7. 1 by 7 into 42, 6 will come. 27.27% I know what this is, below this will be 11 and above 3 will be 3 by 11 What is it? 3 by 11, multiply by 33 means the answer is 9 Your things will be so simple Right? But the point is That we have to learn how to write this and remember it Now actually if you do 27.27 by 100, it will be 3 by 11, after simplifying Right? Now let's try to understand this will be the first step to be faster. Okay. So now let's learn which percentages we can write in which ratio or fraction. Okay. Come on. 10%. It is very easy to find any fraction. 10% means 10 by 100. This is 10%. How much is it? 1 by 10. How much is it? 1 by 10. Isn't it? Meaning, 10% can be written as 1 by 10. 20% can be written as 2 by 10. Obviously, when you are going from here to here, it is 2 by 2, so do it by 2. When you are going from 10 to 30%, it is 3 by 3, so do it by 3. This is 3 by 10. Now it will be bright. If you want 40%, then think directly. 40 by 100, 4 by 10. Or think like this, 10 goes 4, so 1 by 10 goes 4, 4 by 10. Now you will know that this will be 5 by 10, this will be 6 by 10, this will be 7 by 10, this will be 8 by 10, and this will be 9 by 10. And it's not difficult for us to remember. 70% 7 by 10. 70 by 100. 1010. Where you face problems, pause the video. Remove the percentage sign from yourself. Upon 100, you will start seeing. Okay? Now, when 50% 5 by 10 means half. Right? What was 50%, son? Half. 5 by 10 was there. What was 50%, son? 5 by 10, which I can simplify a little more and write 1 by 2 also. 50% 5 by 10 means half. If 50% is half, then what will be 25%? Think and tell me, son. If you have written 50% and 25%, you have done half. So, this half will also become half. And if you do half, then how much will be 1 by 4? You are doing half-half. This too you have done upon 2, this too you have done upon 1 or 2, then it will become 4. Isn't it? So, 25% is 1 by 4, half of half. So, you have 1 by 4. Now, once you have this, you can move on. In fact, you know that 25% is a quarter. Right? 1 by 4. From 25, I am going here, it is multiplied by 3. So, if you go here, what will happen? Multiply by 3, it will become 3 by 4. This will be brilliant, son. Look, son. From here, you went here. How much did you multiply by 3? So, from here, what will happen? Multiply by 3. Similarly, Go from here to here. What are you doing? This is 75.5. So, if you go from here to here, what will happen? This will be 1 by 2. What will be 3 by 4? 3 by 8. When you do half, the denominator will keep multiplying. When you do 2, the denominator will keep multiplying. Say, 25% is 1 by 2, 12.5. 1 by 4 is 1 by 8. If you do half, the denominator will multiply. Now, these are something which you can remember. You can do it. It is not difficult. Look and understand it well. Take your time and pause. See, what is happening? 50% is half, you can see. 25% was 1 by 4. 12.5% was 1 by 8. Similarly, we did for 75 and 37.5. Now see, how can we remember this one? 1 by 7 is 14.28%. See, 7 becomes 14, 14 becomes 28. That's how you remember it. 7 to the 14, 14 to the 28, 14.28% is 1 by 7. 14.28 is 7.14. Right? 1 by 7 is 1 by 14. Initially, it will be a little challenging for you to remember, but you will have to remember. Because with this, all these questions will end up in the air, as you saw. Tomorrow, you will tell me 14.28% of 42. Instead of this, what will I write? 1 by 7. 1 by 7 multiplied by 42. 7 to 42 is a 6 answer. Is it shining or not? That's why we are learning. Because tomorrow when you will be in classes, our regular one, your teacher will write 14.28% as 1 by 7. It will be written in solutions as 1 by 7. If you will multiply 42, you will say, Sir, from where did this come? Now that is why you need to know that 14.28% is 1 by 7. This will be cut. Here, 6 is written directly. And now you are two steps ahead from your fellow mates. The method of memorizing is easy. The 10% line is very easy. It is getting by 100. This story is easy. If 50 is half, then learn from 25, 1 by 4. 14.28, 7 is the table. Remember 1 by 7. 7 to the 14, 14 to the 28. Go ahead. Now, look at these two. Can you see any pattern? Yes sir. This table of 11 is not working. 11, 22, 33, 44, 55, 66, 77, 88. And you have done the same work. You have put 0.B11 in front of 11. 0.B22 in front of 22. 0.B33 in front of 33. And this 9 table is working. 9, 18, 27, 36, 45, 54, 63, 72, 81. Isn't it? And you have put the same table here. 0.18 with 18. Did you see? This is the 11 table. This is the 9 table. Criss-cross it. So, whose table was this? This table was 11. So, write 9 below. Where 11 table will come, write 9 below. Where 11 table will come, what will you write below? 9. That's how you remember it. 11 table means 9 below. I got it right. And where 9 table, when 11 table takes 9, so 9 table will take 11. What will everyone have below? 11, simple, you can remember it, straight forward, Sir, what is the numerator? This is fine, if it was 11, then 9 came down, if it was 9, then 11 came down, Brother and brother interchanged between themselves. Now, if this 11 was 1, then write 1 here, if this 11 was 2, then write 2 here, if this was the third multiple of 11, then 3, if this was the fourth multiple of 11, then 4, 5th multiple is 5, 6th multiple is 6, 7th multiple is 7, 8th multiple is 8. These were the multiples of 9. So, which were the 9's? So, 9 x 1 is 9, 9 x 2 is 18, 9 x 3 is 27, 9 x 4 is 36, 9 x 5 is 45, 9 x 6 is 54, 9 x 7 is 63, 9 x 8 is 72, 9 x 9 is 81, and 9 x 10 is 90. Now, think how easy it is for us. Yesterday, he gave us a question like this. How? 45.45% of 1111. Now the kid will go crazy. He will say, what nonsense is this? 45.45 upon 100 into 1111. I want a calculator. No. Whose is this multiple? 9. If it is 9's multiple, then what will come down? 11. Which is 9's multiple? 5th. So you will write 5 of, means 1, into 1111. How much will it be? 11 becomes 0, becomes 1. 101 into 5, how much is it? 505. The answer is also there, son. You are done. That's how your competitor, your fellow student is faster than you. Because he knows certain tricks which might you are missing. Right? Done? Let's see the last one. 33.33%, son. If you do it by into 3, you will understand. If you do it by into 3, 99.99, close to 100. So, what can be written to it, son? It can be written as 1 by 3. Is it 1 by 3? In fact, you will see it here also. It was 3 by 9. 1 goes, 3 goes. So, how much is it? 1 by 3. This half of this, how much is it? 1 by 6. Then, this half of this, 16.6, this half of this, 8.33. This half of this, 1 by 12. Now, the cat sometimes asks you this one. 37.5 and 8.33. I have seen this multiple times. Right, this is mostly in simple interest and comfort interest because this type of rates can be there. 8.33 Of course, when CAT question comes, it gives a little bit relevant numbers. So, the interest of any bank cannot be that it is giving 25% interest, 30% But it is around 8.33 And sometimes it is around 7.14% interest. That number is given so that you can use 1 by 14. So that whoever knows, can play the game well. So, I hope Guys, the story is clear till here. Right? Now, let's see how we can use them. So, it's your turn. Do this question and show. And now, you know that. Pause and try. See how fast it will be. What is 14.28%? Sir, 1 by 7. Off means multiply. 37.5? Remember. What was 75? 3 by 4. It's half. That means 3 by 8. 75 is not caught, then 50 half, 25 1 by 4, right, 25 1 by 4, 12.5 1 by 8, and this 12.5 3 goes, i.e. 3 by 8, off means multiply, 112, question is over. 7, 8 goes 56, 56 goes 2, 3, 2 goes 6, answer is clear, that is it. So, guys, it is important that you understand that how these percentages can be absolutely converted into ratios. OK, let's go. Let's look at this question. Right, let's look at the problem. Now we will make a flow chart and finish the game. In a city of 27000 people. Okay, there were 27000 people. Slowly, slowly, do it with me, by pausing the video and reading each line. 33.33% For you, this is not there. What is going on in your mind? 1 by 3 I have kept it in mind. If you don't remember now, then write the table I made in the back. Keep it in front of you. Do it by looking at it now. 33.33% For me, it is 1 third. Of the people age more than 40. So, how much is 40 plus? In my mind, it is 33.33%, which is one third. One third of how much? 27,000. It will be overly. How much will you do one third of 27,000? How much will it be? 9,000. 9,000 is over. Now, either you write it here itself into 27,000. But I am teaching you this so that you can do it in your mind. So, then all this will be in your mind. Right? And 44.44% is clear in our mind. What is the multiple of 11? So what will come down? 9. Remember to turn the other side. 11's fourth multiple will come up to 4 by 9. Now multiply 4 by 9 with this. Into 27000. So how much is 4 by 9? 9 is 3. 3000. 3 into 4 is 12000. So our 12000 people are less than 25. Understood? This is the end. Number of people that range from 25 to 40. 25 to 40 people will easily get out. 40 is above 9000. 25 to 12. How many did we get? 21. Total was 27. How many were left? 6000. Out of 27, 21 were left. 6000. 6000 were left in that range. But how could we do this question quickly? Because we knew that this is nothing but 1 by 3. We knew this is nothing but... 4 by 9. If we know that, we are faster. And we can do more questions on the day of exam. Isn't it? Chala jaye. Alright. Aajao beda ispe. Ab ye tumhara. Ek bar pause karo. Try karo. Main hat jaata hoon. Screen se. Try it out. Wapas. Normal sa flow chart and game khatam. Theek hai? Normal sa flow chart and game khatam. Main maan raha ho apne question padh liya. So in a class of 99 students. Aajao wapas. 99 students. 22.22% of students are in red house. Okay. Take out red house students from here. How much is it? 22.22%. You know. 11's multiple will come down to 9. 11's second multiple will come up to 2. 2 by 9 into 99. 9, 11. 11, 2, 22. Red house students are done. 22 is over. Done. Move forward. 27.27% of the students. Okay. Which house is this? Yellow. So, let's write yellow. Now, you know the fraction of this. What is 27? Multiple of 9. What will be the multiple of 9 below? 11. What is 9 3? So, write 3. Now, 11 will be 9. 9 3 will be 27. 27 will be yellow. Right. Read further. 50% of the remaining students. Now, take care of this. Remaining. Isn't 50% total? 22.22% of the total students. Students means total students. 27.27% of students means total students. But 50% of the students didn't write. What did they write? Remaining. So if you write 50% of 19, then everything is ruined. Everything is hard work. 50% of the remaining students. So first make a chain of the story. Now tell me how many remaining students were left. After that, it is important for them to have 50%. Don't do 50% of 99. No, no, no, no, no, no. 99% of 50% of remaining. So first find out the remaining. 99, 27, 22, how much is it? This is 20, 20, 40, 49 is over. 49 out of 99 is left. How much is left? 50 is remaining. 50 students. Now talk. So these remaining students who were 50, 50% of that is half. Which house have these 25 kids? They are in Green House. So, be careful with the remaining. All the questions in CAT will be brought in the picture. We have to remember that whenever we talk about the remaining, we will first make a separate chain. We will first take out the remaining kids separately. After that, the story will run separately in a separate line. Now come ahead. They are in Green House. then find the number of students in blue house. So, okay, I am not telling anything, so we have to assume that there are only 4 houses. Right, so this is red, yellow, green, the remaining is blue house. How many are there in blue house? Obviously, 20. Clear? 25 A.B.Tick. Game is over. I will move once. You see the solution. Read the question. And notice that how I am doing only by making flowchart. No equations. Nothing. One flowchart is going in ratios from our percentage and in one time I am finishing the work. It is going on. Is it clear? Right. Come on. We will take care of remaining. As remaining, flowchart will move forward. Remove remaining and start again from that. Come on. Now let's become a little faster. Question is, what is 20% of 40? You know one. You said, I will write 20% as 2 by 10. You just taught me. 20 by 100 will remain. You will cut 0 one by one. It will become 2 by 10. We are doing into 40. Right. So, one is that I will write its fraction as 2 by 10. Due to which, it will become 4 and 8. Right. But, I have one more faster way. Listen to that. Okay. One more faster way. Listen to that. This method will work till then. First, you have learned the ratio. There is a way to calculate the percentage of 0s. Imagine what is written in 20%? 20 by 100. So, when you have a percentage of 0s, it is written in the last. For example, what is written in 40%? 40 by 100. What is written in 50%? 50 by 100. So, everyone has 0s. Even 20 had 0s. So, 1 0 is not going to be deducted. So, I can't catch it anywhere like this, 4 by 10, 5 by 10, 6 by 10, 7 by 10. And I know what it means, 0.4. What it means, 0.5. What is 60% going to be, 0.6. What is 20% going to be, 0.2. If I had written it like this in my mind, 0.2 multiplied by 40, I couldn't write 8 directly. Because then it would have been fine for me to remove its point, it cut 0, 2, 4, go 8. That means, what would I have written 20% into 40? 2, 4, go 8, 1, 0, 1, 0. This 2, 0, 100 would have taken. Isn't it? How much will be below percent? 2 zeros, 1 zero, take this 1 zero, this is left, 2, 4, 8. If the matter is clear, then look at it again. 30% of 4100. Will 100 come below percent? These 2 zeros must be finished. Let's subtract 1, 1, 1, 2 zeros are finished. What will be left? 3 into 410. Sir, where are these 2 zeros? Take the 2 zeros of percent. Remove this from mind. So, subtract 3 into 410. How much is it? 1, 2, 3, 0, finished answer. Nothing is written. Try one more. 40% of 42, 1 zero. 1 zero is left, now keep in mind. Right, there are no 2 zeros, there were 2 zeros every time, we were cutting. Here also, 2 zeros are cut, cut, 2, 4, 8, answer is there. Now, it's okay, you will keep in mind that 1 zero is left. 4 into 42, how much is it? 4, 2, 8, 4, 4, 16. But 1 zero is left, of the bottom. Put a point, what difference does it make? 168 by 10 is there, 1 zero is left, put a point. That means multiply by 0.4, multiply by 0.3. Point. multiply by 0.2 multiply by 0.6 in 60% if it is 0 then the point will die and if it is not 0 then you multiply it and drag a decimal behind do you understand or not? here I multiplied by 0.2 here it was 0 I removed 0 from the point 2,4,8 here I multiplied by 0.3 it was 0 removed it 3x410 here I multiplied by 0.4 it was not 0 I multiplied by 4 168 came and dragged the point behind here I said I have to multiply by 0.1 I multiplied by 0.1, so 3.3 is here. Or I multiplied by 1, so 33 is here. And I pulled one point back. Isn't it? Because only 1 zero was cut. 1 zero is left. So, think however you want. But you can do it quite faster. Meaning, if you are told 30% of 42. Do 3x42. 3x6, 3x4 is 12. 1 zero is cut. The point of 3 is left. Put it here. Understood? When you multiply by 0.3, you still have a point. Similarly, if we talk about 20% of 810, how do you multiply it? By 0.2. How much is multiplied by 2? 1620. There is a point left, isn't it? Let's put it here. Or think of upon 100 and divide 0 by 0. You can do 81 x 162. Then also 162 will come. If you do the point behind, then also it will come. But you have to be faster. If you understood, then this one is yours. 40% of, let us say, 22. With whom do we have to multiply? First, we have to multiply it by 4. 1 0, 1 0 will be eaten, the remaining 1 0, which will be given as a point. Or 0.4 into 22, which is 8.8. So, this has to be done in one line. Is it clear? I will do one more for you. 30% of 12. 12, 3, 36. 1, 0, 1, 0 is over. 1, 0 is left. That will be the point. Right? Or, it is 0.3, 0.3 into 12. 12, 3, 36. 0.3 was there. 1 point came back. No matter how you think. If you are good in decimal, think from decimal. If you want to divide by 10, think from that. It is the same thing. But, you have to do it so fast. Come on. 1, you start quickly. I will show you all four. Then, I will write together. This is for your homework. Okay? Take your time. Come and tell me the answers. I will know that you have caught it. Do it with shortcuts. Look, in my mind, multiple ways work. Either I will multiply from 0.3 to 0.4. Or I will think that there is a 100 below. Both 0s will be finished. 3, 4, 0, 12 answer. Right? Now, when you don't do 0s, then I will multiply from 0.1. If you do it from 1, it will be 45. If you do it from 0.1, it will be 4.5. What should I do with 15%? Mind your own business, son. You will think of 10% of 42 plus 5% of 42. Isn't it? 15% is done. It is very easy to get 10%. Pull one back. 4.2 is done. Isn't it? 1.0 will be deducted from 0.1. Now if 10% is 4.2, then how much will be 5%? Obviously 2.1. Brother, 10% of something and 5% of something will not have any relation. Absolutely it will. You have increased the percentage. The number will also increase. Isn't it? So, 4.2 plus 2.1 is 6.3. That's it. Done. Now, you can also solve 35 like this. How can you solve it? 30% plus 5%. Right? Whose is to be done? Of course, of 42. Of 42. 30% means to multiply from 0.3. You can do it from 3. How much is 3? 3 to the 6. 3 to the 4. 12. How much do you want to do? From 3? No, from 0.3. This came from 0.3. 5% now, try to use it more. How much is 10%? 4.2. Right? How much is 5%? 4.2 means 2.1. This is it. 14. Now, if you understood all this, perfect. And if it didn't come, then go back and learn this shortcut. Because this is going to make you faster. And these short curves are not limited only to percentage. You will use these in profit loss, simple interest, compound trust. So we have to get our hands on these kind of percentage quick calculations. Yes, you will have calculator in CAD exam, on screen calculator. But again that will take time in such small calculations. We can rely on our mind. Right? Let's talk about percentage increase degrees and then we will do questions. Okay? Let's assume The question is, if 50 to 75 is the number, what percentage is the increase and what percentage is the decrease? Simple thing. How much did you gain by going from 50 to 75? Obviously, when you jumped from here to here, you gained 25. What was the percentage? What was the gain of 25? How much was it? It was at 50. You have to always take the base below. 25 is increased at 50. 25 is increased at 50. So, 25 by 50 into 100. 52 ja, that means you have increased by 50%. Bas. Abhi haan pe apka number chota ho raha hai, to degrees ho raha hai. Kitna chota ho raha hai? Aap 10 se neechay chale gayo. 10 se neechay chale gayo, the kitte pe? 30 pe to. 10 by 30 into 100. And now see your trick come into picture. 1 by 3. 1 by 3 kitna hota tha beta? 33.33% ki to baat ho raha hai. Done. And this time this is decrease. Clear? So, this is your story. Percentage increase decrease. Multiplying factors when you are talking about 10% of something, 50% of something, 30% of something. When you have ratios, you get 14.28%, right? 45.45% and all these things. Let's go ahead and let's see how to assume a number. Now the rest of the things are easy. Here till the base, which is a little typical for children, because it is new. So I hope you have understood till here. If you have any problem in the back area, go back, watch the recording again and then proceed from here. Because now we are going to attempt some problem sums. So fix the back one, set your hands, do all the questions I have done, try them once yourself. Right. Then see my solution and then check. Right. Now see. You will get a question like this. Read the question and pause it. Now this question is very common. The question is, Mr. Rahul gave 30% to Mr. Rora, 50% of the remaining to Mr. Vineet. Mr. Rahul invested the money left with him in a scheme which doubles the money in one year. Find by what percentage the money increased or decreased for Mr. Rahul in entire transaction. Now, in front of the child, a question like this comes in the paper. We have to understand it and do it in two minutes. We have to accept that when the question comes in CAT, multiple scenarios are happening. And we get scared there because we haven't learned to read the question. We run to make a question. Let's assume that Mr. Rahul has X rupees. Then, if he is giving 30%, then 30% of X. and make such big equations. No. When everything is about percentage or ratio, that they had something, gave some percentage, gave some percentage of that, while doing something, it doubled. Everything is in ratio. And then in the last, how much percentage degrees, they finally ask you the percentage. You will take a number and end the game. How? Let's see. First, read this question line by line. Just read this much. Mr. Rahul gave 30% to Mr. Rohra and 50% of the remaining to Mr. Vineet. Okay, so let's assume that Mr. Rahul had 100 rupees. Right? Now see how easy it will be. 30% to Mr. Rohra. The advantage of assuming 100 is that you gave 30% to 100, so 30 to whom? To our Rohra sir. So what's left? You have 70. What's this? Remaining. Right? You must have understood that cat will play remaining a lot. Right? So this work is done. We are a step ahead from the question. The first step of the question is over. Right? Just remember that you have to assume that the one that Rahul ji brought, how much did he bring? He brought 100 rupees in the starting. 50% of the remaining, not 50% of total, of the remaining. How much was remaining? 70. Who will get this? Vineet sir. 50% of this is half of this. Half of this means that Mr. Vineet Sir has got Rs. 35 more. So we have resolved the first line. 30 is given to Mr. Dora Sir, remaining 70. Half of 70 means that Mr. Vineet Sir has got 35. Now the remaining 35 is left. This is the remaining left over. Now let's go to the next line. Mr. Rahul invested the money left with him. Which 35 is left? in a scheme which doubles the money in one year. So, after one year, this money doubled into 2 and today it has become 70 rupees. So, rather than making equations, when you understand all these things and try them yourself, you will see how fast it will be. When the class started, I was solving something. That was the question. And there you will see how I was just writing lines. I didn't have to make a chart. But that will take time. First, let's make a chart and learn so that everything is clear and the notes are good. Right? Two lines have been solved. We had brought 100 rupees. We had accepted this. This was our assumption. Which we know is going to help us rather than making an equation. 30 Rora sir got 30%. 50% of the remaining. Remaining was 70. His 50% was 35. Vineet sir got it. The remaining 35. Remaining. He put it in the scheme. Rahul ji. And it doubled. And it became 70 rupees. Right? Now he is asking, tell me, how much percentage did his money grow or decrease? He started with 100. After all transactions, how much did Rahul Ji get? It doubled, so this is 70. So that means that Rahul Sir is from 100 to 70. The percentage has decreased. How much did you go down? You went down from 30. That means 30% decrease has happened. Another benefit of considering 100. How much has decreased? 30. So if you do 30 by 100, the base is this. Into 100. If you cut 100 by 100, it will be 30%. That means when you consider 100, So, one more advantage is that if your 20 is less in the last, then 20% degrees. If 12 is more in the last, then 12% increase. Whatever number is shifted from 100, that is the percentage itself. Why? Because what will you do? You will write 30 by 100 into 100. This 100 will be cut, right? So, the advantage of counting 100 is that to get the percentage, you have to multiply from 100. Base is also 100. Game is over. 30% degrees. This is your answer. So, a person. Rather than making equations, he is just writing 5-6 words and he is getting the answer. Once he is doing the question on his own, he is not explaining to anyone. He is just laughing, remaining, Vinit, remaining. Rahul does not write this. He ends the game directly. Just like I did on the first page. Now it's time for you to try this particular thing. But take your time, pause it, look at it once, understand it, try it in 2-3 questions and show it. Question for you. Do it brother. Chalo, main maan ke chal raha hoon ki aapne question solve kar liya. To question kera in 2018, 10% of the students left the class. 2019, 30% of the remaining students also left the class. 2020, each student brought another student find the net percentage. Notice karo, wapas saari ki saari baat percentage pya hoon. There is no such thing that 30 students came in a year. These 25 students left. There is no fixed number. If this had happened, there would have been tension. But here everything is percentage. 10% went here, 20% more, 30% more, double, triple. Here you assume without hesitation. I assume and we will direct a little bit. How many students do we have? 100 students. 10% of the students left. You know 10% of 100. 10% of 100 is 10. 10 students ran away. How many students are left? 90 remaining remaining a mess if I live home okay up guys over at 30% of the remaining students right I'm the bad girl 30% of the remaining a semen remaining a guy like so is cut 30% get the other point three right point is a multiple of a 30% a guy the point three into ninety seven a guy took it down in three 27 right or point yes kajal a guy over budget get the 63 So, we reached this line again, that 63 students are left and we only need 2 small tables. So, if we know multiplying factors and know how to convert into fractions, then the game becomes easy. So, I reached here by doing this. First, 10% out of 100, that means 10 students left. 90 students are left. Because, what I am saying is, 30% of the remaining, if you miss this remaining, then everything is ruined. Remaining is very important. Don't miss this word. So 10 ran away, 90 were remaining. What is 30% of this? What is 30%? Multiply it by 0.3. 0.3 x 9, 0 is deducted from 0. 9 x 3 is 27. 27 ran away more, isn't it? How many are left? 90 minus 21, that is 63. Now, in 2020, every child went and brought another child. So 63 children, 63 children must have brought more. Every child brought one. What is the net? 126. Now, what is the net percentage increase? From 100, If you have reached 126, then you have increased it to 26. And 26 means 26%, 100 means 100, you know that. Done. Again a simple flow chart and you are done, absolutely done. This is the power of flow chart. If you understand, then write it once that yes sir understood. I will understand that you have understood, right? And if you still have a little doubt in this, then go back. Try both the questions again. See what is happening again and it will be absolutely clear to you guys. Okay? Let's do one more question. You answer this. Okay? Pause and try again. I will leave now. Now we will assume the numbers properly. And this time, that number will not be 100. Why it will not be? How did you know? That will also be understood. Read the question first. Okay. I assume you have read the question. In a school, a student can score grade A, B, C or D in a test. If 14.28% of the students got A grade, very good. 22.22% of the students got B grade, very good. 20% of the remaining got C. Remaining is brought, keep this in mind. Find the approximate overall percentage of students who got D grade. Sir, we will assume that all are percentage. It is true, sir. It is necessary to assume. It is all about percentage. Assume is a must, no doubt. But, if you have assumed 100, then see what happens. 14.28% of the students. Now what will I say that 14.28% of the students were in grade A? This will start getting tense, who will do this calculation? We were assuming because the numbers are good. Now we have to do 100-14.28, will 22.22% of that be good or not? We will get stuck. I was not having any problem in life till now because if you notice in the questions at the back, I was not getting good numbers like 10%, 30%, 20%, 40% type numbers. I will assume 100 and move on. Now see one thing, how do I assume the number well? Listen to me. 14.28% how much is it? Is there any strike in your mind after seeing this number? You should do it. What is striking? Sir, 1 by 7 is striking. This was 1 by 7. 22.22% is striking in your mind. Yes sir, this is 11's multiple. So, sir, 9 will come down. 11 goes 2, so 2 by 9 will come. So, I have come to know that I have two fractions written. Taking out 14.28% means I have to multiply the number by 1 by 7. So, when I am assuming, if I assume 7's multiple, won't I get benefit? Means, when I was assuming 100, and its 14.28% means 1 by 7 multiplied so 1 by 7 into 100 was not a good thing but if I assume 70 instead of 100 then 14.28% would have been easily taken out in 1 by 7 of 70 When you know which percentage you have, and who you have to multiply, then you can put a number here that is less than 7. So that this number is good. And when I know that I have 7 and 9, I can handle this 20%. When I have 7 in the denominator and 9 in the denominator, then I can put a number that is less than 7 and 9. What is the number that is less than 7 and 9? Multiply these two. 7 is 9, so 63. Now, I will assume the number 63 and my question will be easy. But how did I think? I looked at the percentages. The denominator of the fractions of these percentages, listen carefully, the denominator of these percentages, when the fractions are written, the denominator that was being given, we have to assume the number that is deducted from that. And the number that is deducted from 7 and 9 is 7 into 963. So today I will assume that my number was 63. Now when 14.28% of the students got A, 14.28% is 1 by 7. Multiply by 1 by 7. How much is it? 9. Easily got it now. So 9 got grade A. How much is 22.22%? Sir, 11's multiple is 9. 11 to 2 means 2 by 9. Multiply by 9. 7 to 2. 14. What did you get out of 14? B. And 20% of the remaining. So first go to remaining. How much will be remaining? 14 and 9, 23. Total 63. 63 minus 23, 40. 40 is remaining. Now remaining 20%. 20% is to be multiplied by 0.2. Point will be deducted, 0 will be deducted. How much will be? 8. Right. That's why I am saying 20%, 14.28%. Which means 8 students got D grade. Point the approximate overall percentage of the students who got D grade. How many students got D grade? 8 students got D grade. So, 32 students got D grade. And, he is asking us how much percentage of students got D grade. So, 32 students got D grade. So, 32 students got what percentage? Overall percentage. So, overall students got 63. So, 32 by 63 is what percentage? Do it into 100 and get the answer. Sir, who will do this? Who will do 32 by 63? What are you saying? Use your brain. Even if there are options, it's part of the question. Can't I approximate? If it was 64, it would have become half. Would it have become or not? And what would be half into 100? 50%. This would be very close to 50%. So what is this option doing? This is not in the picture. No problem. It's very close to 50. Half is written almost. But sir, all three were near 50. How can I find out? Think about it. Is this half bigger or smaller? Obviously, half of 63 is 31.5. If it was 31.5, you would have got exactly half and 50%. This time, you are slightly bigger than 31.5. That means the answer should be bigger than 50. What is the half of 63? 31.5. If it is more than 31.5, then it is more than 50%. And if you are below 31.5, then you are below 50%. You are more than 31.5, you should get more answers than 50%. These two are below 50%. The answer is over. Use options. Yes, if there were 3-4 options above 50% and close by, then we would have been stuck. Then we would have to pick up the calculator and do it. But still, this story happened so easily. Now, he was explaining it. Otherwise, I would have explained it, I would have accepted Direct 63. Why? Once you understand these things, you will become faster. And if you try to go back the conventional approach again, yes. It will be easier because you already know it. That is nothing new for you to learn. But you will be slow. And by the end of 7-8 months, when you will be near to CAT 2024, then you will realize that you should have learned it. So even if it takes time today, you have to see one method four times. But learn it. Because it will not only help in percentage, but in the entire application of percentage. Which is simple interest, compound interest, profit and loss. Even mixtures. Okay? Let's go guys. Now, jump to the third topic that is Assumption plus Unitary Method. Abhi tak aapke question ko jis tarike ke dikhte the. Right, we did this question. See, isn't it? We did the same question. Rahul gave this, this, this, that, right? Everything was in percentage. Now this time, there will be a slight change. What will be the change? He will remove this last line, right? And instead of the last line, he will do something else. Like this. Here is the seam. But in the last line, instead of asking how much the net percentage has increased or decreased, he will say that Mr. Rahul is left with 1050 rupees. Now tell me how much he brought. Right? Now let's understand how to do this. Don't be afraid. As soon as you see the question like this, Percentage, then percentage, then percentage. Right? We will play the game. He was giving us the tension of 1050. The new one, we will see that later. You solve line by line. Let's again start the game. Mr. Rahul gave, I will assume again. I will assume the same as before. One step will increase, nothing else. What did I assume? That Rahul ji, he 100 rupees lekar aagay. So, ae baat hai. 30% yunne Rora ji ko diya. To Rora ji jo hamare hai, wo 30 rupees leke chale gaye. Remaining hamare paas baj gaye, 70 rupees. Bohot bhiya. Shahbaz sir. 50% of the remaining mele Vineet sir ko. To Vineet sir jo hai, wo 35 leke chale gaye. Aur ab jo inke paas remaining baj gaye hai, left mai likh deta hu, wo ho gaya 35 rupees. Ye to humne peechay giya. He invested it and it doubled. And today, Rahul has 70 rupees. Till here, there is no tension in his life. We know to do assumption. This part of our question will be step 1. Which is called as assumption. This part is over. Now see how the unitary method will look. Now the question will be, Mr. Rahul is left with 1050 rupees. How much money did he have in the beginning? Now listen to this carefully. There are two stories here. One, which is our assumption story. One, which is our real story. Is that right? And two things are important for us. One, how much money did Mr. Rahul have left after doing all the stories? That is, how much left money does he have after doing all the stories? And the second important story is, how much money does he have? in the beginning. Why is this important? Because in the question, one of them is giving and the other one is asking. These two will be important for me. One will give value and the other will ask. These two are important. We will match these two with the ratio and unitary method. Now let's see which two quantities are important in the sentence. The one who is giving is left with after doing everything. The other one who is asking in the beginning. So I wrote both of them. Is this a real scenario or an assumption scenario? What do we know? We know everything about assumptions. You can ask anything, but we know everything about assumptions. Let's look at it according to assumptions. After doing everything according to assumptions, Rahul Ji had 70 rupees left. And how much was it in the beginning? 100. That means, its ratio is 70 by 100, 7 by 10. The ratio will not increase without increasing. Now talk about real scenario. What do we know about real scenario? There were two things in real scenario. One will give and the other will ask. So, the one who will give, he knows. What is given in this? 1, 0, 5, 0. In the real scenario, he is telling us that 1, 0, 5, 0 rupees. 1, 0, 5, 0 rupees. In reality, he had saved it. Is it true or not? Clear? Done? Now, finish the game. Now, finish the game. You have to get only one thing, the beginning one. How will you finish it? This upon this is equal to this upon this. Bro, their ratio will remain the same. Everything is in percentage. If you had brought 100, then 70 would have been left in the last. How many would have been brought? That 1050 would have been left. So this upon this equals to this upon this. How did you do it? You know everything about assumption scenario. In real scenario, one thing will give a question. One thing will ask a question. What did you give? How many are left in the last? What was he asking? The beginning one. So these two quantities. entity considered given 1050 asking x assumption 70 left 100 this is your second part and this is the most important part this is your unitary method it will be solved easily see cut this 0 0 cut this 7 7 1 7 5 15 16 So, x will come here and this will go here. Solve it easily, x will be 1500. I have a little space left, but you solve it. This 7, 15, 105, x here, 100 x 15, 1500. Take 1500 rupees and the game is over. The same scenario that you know, one thing is being added at the end, which one? Comparing the entities. Which entities? One who is giving, the other who is asking. Use the unitary method, the game is over. You will always know about assumptions, because you have resolved the whole scenario of assumptions. Here, one of the two is giving you, that's why the other is asking. Done. Do one question by yourself. I am keeping it at the back. Pause it once. I am on the side. Done. Now this one is yours. Try it. Okay. I am going to do it. Again the same scenario. There is a class. Some 25, some percentage. I am not asking the percentage at the end. Last, I said find the number of students in the class if the number of students in the green house were 56. So, remove this line. We will add this last when we have to apply the unitary method. First, you assume the question to be simplified and solve this much. Do the assumption part. We will see the next part later. So, let's see the assumption part. In a class, a student has the option of choosing one of the four houses. Very good. 30% 20% As long as it is 10's multiple percent, 100 people are not a problem. So, we said our class had 100 children. Alright, 30% of the class chose red. 30% how much is 30? So, which 30 children do we have? Red house children. Very good sir. 20% of the remaining class has yellow. Okay. Now, remaining is saying, son, we have to stop. If you write 2020 of this, everything will be over. Everything is wasted. Money is wasted. Right. So, that means we have to wait. How much is remaining? 70 is remaining. Now, let's run this story separately. We had 20% remaining. 20% of this means, multiply by 0.2. Right? 0 will be deducted from 0. 2 times 7 is 14. How many of these 14 are there? Yellow house ones. Okay. If the number of students who chose blue and green are equal, are the blue and green equal? So, how many are left? 14 out of 17, which is 56. And 56 is divided equally between blue and green. So, 28 is blue and 28 is green. This is the end of your assumption part. Congratulations, you are 70% done. Now, 30% will come from the last line, which is your unitary method part. So, get ready. Everything should be comfortable till here. Right? Now, let's see what he is giving us and what he is asking us. This is confirmed. One will be our assumption scenario. One will be our real scenario. Right? Now, one of these entities will ask us, and one of these entities will give us. Correct? So, let's see what he is giving and what he is asking. Come on. Find the number of students in the class. That means, what is asked is the number of students in the class. Right? So, one thing happened, the one who is asking us, that is the number of students. Now, if we talk about the number of students in the class, then we know in the assumption. How many did we consider? 100. How many in reality? We don't know, that's what he is asking. Now, what is he giving? If the number of students in the green house, which one is it? Green house. How many are there in the real scenario of the green house? 56. According to our assumption, how many are there in the green house? 28. Are you done, son? You are done with the unitary method. Wait a minute. Now, here it is happening like this. 28 goes to 2, so 100 goes to 2, i.e. 200. Or if x goes here, it goes there, so x comes to us. Sometimes the directives are 2x2, so this will also be 2x2. 200 answers, you are done. It's that simple, guys. Chart, 70%, 30%, unitary method, you are done. Take your time. I didn't know that I am green or number of friends. It's possible that I would have compared yellow if he would have given me given number. Here, yellow is given. Same scenario, in fact, if you see, I can make 5 questions from this question. In fact, if you print a book, you guys sit and print a book. Keep changing this thing here and the book will keep on being made. 5 questions will be made like this. Should I show you the rest? Yes, show me. Does the question look the same? Read it. It's the same, sir. No. From here to here, the story is the same. This time, the point is the number of students. I asked again the same thing, but the given thing changed. If the difference between the number of students in Greenhouse and Redhouse was 6, that means, whatever change will come will only come in my unitary method. One scenario will be of assumption. One scenario will be of real. What is it giving this time? Numbers, functions, greenhouse and red house's difference. Right? Greenhouse and red house's. Difference, means the difference between green and red is given in 6 real scenarios. And it is asking the total students which is x. In the assumption part, you must have been champs till now. In fact, the question at the back is the same. What was it? We had accepted 100 children. Out of 100, which one did we put 30 in? In red. Out of 70, how many children were left? 20% out of 70, means 14 children were left. They were in yellow, the remaining 56 were equal to green and blue, that is 28 and 28. This scenario is exactly the same as I gave you in the previous question. Now, the given thing was something else, maybe it was the children of green house. Today, I am giving you the difference. So, let's see what is in our assumption. In our assumption, the total is 100. And the difference between green and red, number of students in green house and red house, see how much is it. 30 in red. Green by 28, how much is our difference? 2. This is as per assumption. 2 is going to go, 3 is going to go. So, how much will 100 go? 3 is going to go. So, x is 300. Game is over. So, if you can view that, fine, visualize it, fine. Otherwise, upon this, upon this, equate it. So, 3 is going to go, x is going to go there. And this 100 is going to go there, x is 300. This is what you need to learn. Here, I am not going to make equations by taking x, y, z. This is what we have to learn, no equations, no. You will solve such big 5 line questions, right? Now you will do it yourself. You will make a table and go there and solve it, isn't it? Come on, son, this is yours. Out of the shirts produced in a factory, 15% was this, 20% interest was this. Remaining 88040 are left for the export then the number of shirts produced it. So let's forget this part again. This part will be used in the unitary method. Solve the story till here. Right? 15% and 20% are good, 100% will do the work. You start with your assumption that is you had 100. Pause after doing it. And wherever you get stuck, play step by step. Not that your answer didn't match, then play it completely. No, step by step. As soon as you get the mistake, then stop and do it yourself. 15% means 15% is defected While 20% of the rest, rest means remaining If it gets messed up, then stop How much is rest? 85, your rest is 85 What is their account? 20% of the rest are sold in domestic So this rest is for sending them, domestic 20% means, tell me how much is it? Sir, multiply it by 0.2 Multiply 0.2 by 85, how much will it be? 170, 1 zero will be eaten, 17 will be left. 17 were in domestic. And what else did you do? You exported, obviously. So, out of 85, how much did 17 get? Out of 75, 7, 68. 68, you exported. Correct. Assumption that the story is over. Chain is over. If you have done it till here, then you have understood 70% of the story. You will do all the percentage questions. But you will not be able to apply the unitary method. We will see that now. Right? Now read the remaining and see if the method is looking like a reunitary method. Check it. Should I apply it? Let's go. Again, we have an assumption scenario. We have a real scenario. Let's see which quantities we have to see. One will be given and one will be asking. Right? Let's go. Check it. If the remaining 8840 Shirts are left for export. Which is the given quantity? 8840. Export ones are giving us. How much is the export according to real? 8840. According to us, how much is the export? 68. Alright, very nice. Go ahead, Gani. Then the number of shirts produced, which is the total. The total is asking which is X. According to us, the total is 100. Finish the game, guys. We will have to beat them, but the answer will come. Cut a bit according to yourself. I will cut it. Okay. I will help you. So, this upon this equals to this upon this. It is going from 17. 17, 4. 17, 5. 85, 334, 520. 4, 130 will go. X will come here. Equals to 100 will go there. 1, 3, triple 0. If you have got the answer, congratulations. You have just done a CAT 2017 question right now in your very first class. If you could do it. So these kind of questions are definitely going to be there. Direct CAD ka sawal. Sirf aur sirf ek chhoti si cheech pe. Kya? Yeh. A good assumption. Make the scenario. Unitary method. You are done. That's how you do the questions in 30 to 40 seconds. Believe me, once you have the habit, yeh sab likhne mein apko time nahi laga hai. Toh main samjha raha hoon. Aap rukh rukh kar rahe hoon so it's taking time for you. But when you become a pro, these all the things are just very very quickly done in the exam. Right? So, guys, today's class is over. I will explain you a small part of multiplying factor. Let's finish the game. So, if I say 10% more than 300, what does it mean? Let's understand. It means that you have 300 and 10% more is added. So, whose plus 10% is added? 300's. This is the meaning of this statement. Or you can say 300 is increased by 10%. This is also the same thing. 10% more than 300 means 300. This is it. Plus 10% more. Whereas, if it was happening in this way, 10% more than instead of this, I would have written 10% of 300. This would have been a very different thing. What would this mean? This would have been 0.1 or 10% multiplied by 300. That's it. This and this are very different. Right? 10% of 300 was just this. This has 300 already. 10% more has been added to that. Is it clear? So, 10% of 300 is a different story. 10% more than 300 is a different story. So, this is 10% more than 300. Now, there are two options. Either you solve it. 300 plus 10% is 0.1. Multiply by 300. You have learnt this. Now, you will take this 300 plus 30. And you get 330. So, one is this method. But we are not going to do this. Now, let's go to another angle. If you take 300 as common, then what will be left? 1 will be left here. 10% will be left here. What is 10%? 10% which is nothing but 0.1. You know what 10% is. 0.1. Or you can see here, 0 to 0 will be 0.1. That is 1.1 into 300. This thing is called as multiplying factor. Now, see how useful this is. I have... This is all drama. What was the meaning of 10% more than 300? 1.1 into 300 I could have directly written that. Think about it. 10% means 0.1300 has increased. 1.3 is already there. 0.1300 has increased. So, how much is it? 1.1 or not? 1.3 was already there. 0.1 of 300 is increased. So, how much is it? 1.1 That means, if you tell me tomorrow 20% more than n. I will say 1.2n. That's it. It is n. 20% means 0.2n has increased more. Now 1 was there. 0.2n has increased more. 1.2 has increased. See. 1 plus 10%. What happens there? 1 plus 20%. 20% is 0.2. 1.2 does not happen. Similarly, if you tell me 35%. More than n. So, it is 1. Plus how much are you getting? 35% which is nothing but 0.35. Meaning 1.35n. If you get it right, then it is very good. You can solve all these equations like this. 10% more than 12. How much is it? Sir, 1 was there. 10% means 0.1 more. Meaning 1.1n. How much is 12? n is 12. How much is it? 11, 12 goes to 132. 1 decimal is 13.21. Next, 20% more than means 1.2. 1 was there, it will add to 1. How much will it add? 20%. What is 20%? 0.2. Add to 0.1, 1.2. Into 50. How much is it? 60. 70 is increased by 30%. That's the thing. This means 30% more than 70. 70 is the same. 30% has increased more. That means how much? 1.3 times. Whose? 70. Point will be removed. Zero will be removed. 13, 7, 9, 11. 20 is increased by 26%. That means again, 26% is increased. Who is 20? 26% is increased. That means 1.26 into 20. Now, multiply it by 2. How much is it? 252. 1 is 0. 1 is a point. 1 will increase. Then also, 1 point will remain. 25.2. Game over. Done. That's how you will finish all these things if it talks about percentage increase and degrees as well. That's all you have to do. If you understand this, then degrees are very easy. Same thing, what does 10% less than 300 mean? Something has gone from 300. How much? 10% of 300. Means, if 300 is common, then the first one which was being added, is being minus 10%. And 10%, you know, is nothing else. It is 0.1, which becomes 0.9 into 300 now. Now, I would have written directly from here. Means, if you tell me 20% more than n, then I will write 0.2 into 1. add and what I say in mind is 1.2n. This happens in my mind. Now if you say 20% less than n, then I do 20% out of 1, which means 0.2 minus, which becomes 0.8n automatically in my mind. So if you increase 30%, then 1.3, if you decrease 30%, then 0.3 out of 1, which means 0.7 is left. The story will run from 1. If you increase, then I will increase from 1. If you reduce it, then I will reduce it from 1 because it was that much. I had brought 300. According to that, I went up or down, so 1 300 is there. Right? Clear? See it once comfortably, it will be done. Then apply it after that. 10% less means, 1 was there. 1 minus 10% is how much? 0.1. Will this happen in my mind next time? I did it for the first one. 1 minus 0.1, 0.9 into 12. How much is it? 108, 1 decimal is 10.8. 20% less than 50, how much is it? If we did 20%, then we have 0.8 left. From 1, we have 0.2. Into 50, how much is it? 40. 70 is decreased by 30%. That's the thing, that 30% is less. If 30% is less, then how much is it? 0.7 is left. If it was more, then it would have been 1.3. Into 70 equals to 49. I'm leaving the last one for you. Do it and let me know in the comments. Yes, sir, we learned. It was fun. We broke a lot today. Now this increased degree will help you a lot in the application when I will bring the next lectures. SICI Profit and Loss. How to get a certificate in percentage? Watch. Question will be made in one line. Game over. Always study line by line. The whole question never increases together. I scored 40 marks. After review, every marks were increased by 40%. If something increases by 40%, then what is multiplied by? 1.4 multiplying factor. This is the multiplying factor that you multiply. 1.4. Son, there was 1. If you are increasing, then move forward. How much to move forward? 40% means 0.4. How much to move forward from 1 to 0.4? 1.4. If you take 40% back, then 0.4 has to go back. From 1 to 0.4, it went back 0.6. That's it. So now that's it. First it was 40, 40% increased. Even after that, it failed with 4 numbers. How many have it come? It has come 56. And still it has failed with 4 numbers. So if it had come 4 more, then it would have passed. That is, 60 have become your passing marks. Game kata. Itna simple ho jayega. Question bus dekhne me difficult hai. But if you know the multiplying factor, percentage ka game kata hai. Agar mai apko ek quick revision do, to humne jo aaj mota mata sika. Ek to aapne sika ki percentage ko fraction me kaise leke jate. Wo aapko yaad hain nahi hai table. Right. Doosra jo main mudda aapne sika hai. That is 20% of 40 ki baat karo. So this is 0.2 multiply by 40. Which is nothing but. If you do 240, it will be 80 and it will take 1 point decimal. One thing is 20% more than 40, which is 20% more. 0.8 in 1 means 1.2 into 40, which is 48. And another thing is 20% less than 40. Now, if 0.2 goes from 1, then how much will be left? 0.8. Decimal will be this, 84032 will be taken. right. Then you have understood how to assume plus how to apply unitary method. Done. So, guys, this is it. So, this is the start to a new revolution, where you do not have to be afraid even if you are a newbie to quant. You understand that yes. It's not going to test you on higher mathematics. It's going to test you on the basic things which you also know. So if you think that only IIT and C can score, or only engineers can score well, or only those who have prepared for a competition can score well, then you are wrong. Because the concept is the same which everyone knows. It's just that because they have prepared for any competitive exam, so it's a little fast. They have the other approaches. We are going with the same traditional approaches which we had learned in our childhood. Which one? Accepting X, accepting the equation. but the game is not there. So, rather than assuming x, y, z and making equations and spending time, right and giving a chance to you know big equations can also lead to sometimes silly mistakes. We are going to apply such approaches and be faster. So, before you start your preparation, understand that it is a game of aptitude. And we will use such scenarios and such approaches in life classes. So, if you already know them, then you will start on the same line. Whether it is an IITian, a commerce student, an average student, a good student or a mediocre student or even less than mediocre student. So, once you have all the same line, then there is no excuse to ask for. You have all the time. revise all these things, see all these approaches which you might take in the classes. So that is it for today. This is your quant mentor Rahul Bhatla signing off and let's continue this revolution with the upcoming classes. Take care. Bye bye and have a great day.

1 by 7 multiplied by 5 by 9 into 63 is equals to 5. Arey, aap log aage? Welcome to your pyarasa channel MBA wala. Welcome to your batch CAD essentials.

Welcome to a revolution. Kis cheech ka revolution? Chalaiya jaante. Toh for all CAD 2024 experience.

Guys, first of all, this is Rahul Bhatla, your quant faculty from MBA wala channel. Now we will start a revolution here. We will teach you essential things which are necessary to start your CAT journey. Otherwise, many times they make you lose a little bit of confidence in between.

If you don't know the basic things, sometimes they off track you from your journey. You start getting scared. Why?

Because you have competition with students from all over India who are aiming for CAT or CAT exam, IIMs or good business schools. Now what happens is that, Here you will find some people who are extraordinary better than you. Right. Some people who are like you.

Some people who are a little weaker than you. So if you are a student from average mathematical background or below average mathematical background, then what happens is that we do not understand some basic things. It comes out of our mind. Or we get concepts, but we are not able to apply those tricks.

And some children who are actually good in quant, good in mathematics, they forget that this is not a math exam, it is an aptitude exam. Right? You study well, after 8 months you learn concepts, then what happens is that when you go for mock tests or you go for sample questions, the questions are being made, there is no problem. But in those 40 minutes, you are able to do only 9 or 8 or 10 out of 22 questions.

And because of that, your score does not come. And then you keep thinking that how are they doing the questions that their question is so fast that they are able to make it up to. 14 or 15 questions. Whereas, ours are only 8 or 10. And the difference is in the percentile. Whereas, when we get all the math, then we start looking for the problem.

The problem is guys, approaches. So, this CAT Essential Series, the upcoming series, which is going to target 100 percentile for you, is the base, is the foundation, which will help you know that what are the approaches, which we use in CAT Quant. What are the aptitudes we apply in CAT Quant?

You will know today that this is not a maths exam, this is a quant aptitude exam and there are approaches which will make the questions look easier and by which you can do the questions within 30 seconds, 40 seconds. The questions which look very big. For instance, I will give you one more example.

This was a simple, right straight forward equation. Let us see a problem solving question. This type of question.

Invest at the left. Now, after reading all these questions, it takes us at least 1-2 minutes. Because we are following standard mathematics, we are accepting x, we are accepting everything, we are accepting y, we are making z equations.

But after today's class, how are you going to do this question? Do you want to see? Look guys, I am going to learn this question.

Now, whether you understand or not, it doesn't matter. We are going to learn all this. If I were in your place, I would have done this question in such a way that I would have assumed that Mr. Rahul had 100 rupees. 30% was given to Rora sir, so out of 100, 30 was left, 70 was left. 50% remaining Vinit sir ko de diye to 35 aur chale gaya, bache 35. 35 ko invest kar diya aur wo double ho gaya, yaani ki ye ho gaya 70. Ab 100 leke aya the 70 tak poch gaya, yaani 30 niche chala gaya which is 30% decrease.

Itna likh raha hai ek bacha. That is why he is able to do questions in quick time than you. And if you are following this approach, perfect.

And then we have many more planted for you in this particular session. Jisko nahi samajh mein aaya, that means a lot to learn for you guys. I mean, today we are going to learn a lot. So, fasten your seat belt and let's get ready. Again, a very warm welcome to the first session of CAD Essentials.

We will talk about Quant Percentage. Today we will talk about the whole thing and we will talk about the lecture number 1. Myself Rahul Batla, your Quant Faculty. Okay, let's start the game. First, we will learn the basics. I will take the tricks from the basics till the end.

I will also show you some of the PYQs of some of your CAD. And by the time you go, you will also be so fast that you will be able to solve the question by assuming a good number. Remember, I will not assume 100 every time like the last question.

So, till now, the talks are done. Let's start the game now. Come on, son. Topics.

Percentage and ratio. How are they related? What happens? Is percentage and ratio the same thing? We will talk about all of them.

How to assume a number? How to assume a number? Right? Assumption plus unitary method multiplying factor.

This is the main topic of our class today. The key topics which we are going to cover are these four. Let's start the game. Here is the first game. Percent.

What does it mean? Very basic. Per means something divided by.

Cent means century. Hundred. It means how many out of 100 are there? For example, a child brings 10 numbers out of 20 numbers. If it continues at this rate, then how many out of 100 numbers will it bring?

Sir, it's a very simple thing. This is multiplied by 5, this will also be multiplied by 5, which means 50. That means 10 by 20 is nothing but 50%. Now this is logically reached, from aptitude, but actually we will not keep taking it out like this, so how will we go? We will see that, but now what does percent mean? How many out of 100 do you bring?

10 out of 20, okay? But if it was out of 100, then how many would you bring? The thing is that you used to bring 10 out of 20, half, so you will bring half out of 100, 50, that means you have 50%.

Right? Now, percent benefits us in comparing, in finding out, for example, I said one kid's number is 100, one kid's number is 200. Who scored more? You will say 200 kid did not. Which kid is good?

200 kid did not. Did you know the total marks? You did not know. So let's assume that this kid got a total of 200. And this kid got a total of 200 out of 500. Now who is more?

Now it seems that the 100 number player is good. Now that's why we said that you will know if you take it out in percentage. Now to calculate the percentage, we do a simple thing.

We multiply 100 on both sides. Here also multiply 100 and here also multiply 100. This will give you the percentage. Now if you solve this, it will cut 0 from 0 and 0 from 0. This will be 50. That means, the child who got 100 out of 200, this child's result is 50%. This guy is equal to nothing but 50%. Here, this is cut, this is cut, 520 goes.

This child's result is 40%. Which child is good? Obviously, the child with 50% wins.

And what does this mean? This means that if this child gave a paper from 100 instead of 200, then he would have got 50. Means 50% 50 per 100 Today I have come with 100, but if the paper was of 100, then he would have got 50. Similarly, he brought 200 number from 500, but if the paper was of 100, Today I have come with 200, but if it was of 100, then he would have brought 40. That means 40 Per 140%. This is the meaning of percentage.

And along with that, you have also learnt to calculate the percentage. Now, you are going to get two most common statements. One is this.

What is 10% of 40? Right? How do we solve them? We learn to solve them. This is the meaning.

Now, what is 10% of 40? Let's understand. If I ask you, what is 10% of 40?

See what you have to do. Say simple. 10. Write 10. Percent.

Per. and cent, 10% off means multiply 40 means 40, this way we will get the percentage easily 0 will be deducted from 0 0 will be deducted from 0, you will get the answer as 4 Now we will get fast in some time that I will convey all this without writing the answer but first basic should be clear otherwise you will not be able to understand the tricks Once you understand the basics, then it is easy to learn the tricks otherwise you will have to keep the tricks and you will not remember the tricks for long time but if you understand then the tricks will always be with you all life long What is 20% of 30? Again, the same thing.

Will you try it by pausing? I am doing it. 20 per, percent is read, so, per cent into 30. How much is it? Again, 0 to 0 is cut, 0 to 0 is cut, that is 6. What is x% of y? That means, x per cent of y.

Did you understand? So, percentage sign will be removed, upon will be 100, off means multiply, y. Now, x, y, whatever happens, you will solve it.

So this is the first thing we should know. Second is something like this. If you get 100 out of 200, then what is the percentage? So 10 is what percentage of 40?

Simple. 10, what is the percentage of 40? So you write 10 by 40 and multiply by 100. Like 100, what is the percentage of 200? You wrote 100 by 200, you multiplied it by 200. What is the percentage of 200 by 500? You wrote 200 by 500, you multiplied it by 200. 10 by 40 is 10 by 40 into 100. How much will it be?

It will be easily deducted. It will be deducted from 0 to 0. It will be 25%. So, you should know two things. One, to get the percentage. If you have 100, how much is the percentage from 500?

And one, to get a percentage of any particular number. To get a percentage of any particular number. Like, what is the percentage of 40 to 10?

This should be known. Only then we can move forward. Right? It is possible that you say, 20 is what percent of 50? So, 20 is 50. How much percent is there?

Into 100, game over. 52 will go, you will get 40%. Similarly, x is what percent of y?

So, x, y, how much percent is there? Game over. Am I clear?

Once you note it down, I will move away. These two things you should definitely know. What? How to get a specific percentage of something.

Second, how much is 1040%? Right, how much is 2030%? Like that we are going to do. This was a meaning story. Percent means something upon 100. How many out of 100?

Percent, per 100. And the other story is this. Now let's become a little faster. Let's understand what is ratio, how percentage and ratio are related. Let's assume we have a beaker. In this beaker, 100 liters of mango juice is kept.

Now a child came, he threw half a mango juice. Half a mango juice means, obviously, how much he threw? 50 liters he threw. Now see, there is one child who is telling us that you threw half a mango juice.

If you... If you throw half mango juice, you have only half left, that means half is left. And one kid is saying, I am not telling you that half is left, I am telling you in percentage.

He is saying, you threw 50 liters, 50 liters are left. He is saying, sir, 50 is left. From how many? From 100. How much percentage is left?

50 upon 100 into 100. You have taken out percentage like this. Something, from total, into 100. He took out this, that means 50%. Now one kid is saying, sir, 50% is left. One kid is telling in ratio that half is left.

Both are right. Absolutely right. One person is telling the ratio that half is left.

One child is telling the percentage that 50% is left. That means ratio and percentage are interrelated. And half is 50%.

How can you see? If you simply multiply the ratio by 100, then you will get the percentage. Now if I know this, it will be very beneficial for me. Because if someone told me yesterday 50%, right?

Someone told me 50% of 21. Now if I take the percentage in ratio, it will help a lot. 50% now I am doing 50% into 21. Now I can do it in my mind. 50% means half. So I am writing it straight.

I am thinking about it. White line in my mind. 50% means half of 21. How much is it? 10.5.

Half of 21 is left. 10.5. That's it.

So sometimes your percentage will help you. You will say sir 50% would have been like this also. I would have done 50 by 100 and it would have worked. But if the question becomes like this one day. 14.28% of 777. Now one child is stuck.

Why? Because he is doing this calculation. 14.28 upon 100 into 777. It worked. So aha!

Now either he opens up the calculator or he is done with the question. Now, the second person who knew that the ratio of 14.28% is equal to 1 by 7. Like you knew that 50% is half. The person who knew 14.28% is 1 by 7, will do 1 by 7 into 7 is 77. He will also do this and the answer will be 1 by 1. It will be cut.

That means if I know the fraction or ratio of percentage, then the question will be easy. In fact, we make the question from here. So if you solve this using a calculator, 14.28 upon 100, it will automatically come to 1 by 7, very close.

14.28 multiplied by 7 is 100. So approximately 14.28 is 7 over 100. That's how we work. Now we try to learn few percentages whose ratio is good. Like 15% becomes half.

14.28% becomes 1 by 7. How can I remember all these? Is there any trick? Let's find out.

It will be very beneficial. Because yesterday I asked 14.28% of something. 14.28 is very difficult to handle. Instead of that, I will write 1 by 7. Game over. Check it.

Come. I will show you some questions and I will tell you how I do it. Then I will teach you and then you do it.

I would have written 25% straight. 1 by 4 into 40. This is what I am thinking. And the answer would have been 10. Now how did I write this like this?

I will teach you this now. Actually what I am doing is, what do you do with 25%? 25 upon 100?

And what does this become? 1 by 4? Is it true or not? I would have done this.

Similarly, 33.33% I know 1 by 3. 1 by 3 of 45, I write 15 directly. Now how did you do this, sir? Son, I knew that 33.33% would become 1 by 3. Sir, how did you know? Son, when you will also see, then this 33.33 Upon 100, when you will do, 1 by 3k procs will come.

I will teach you. You will also remember. But see what is the benefit of them first. 14.28%, I know it is 1 by 7. 1 by 7 into 42, 6 will come.

27.27% I know what this is, below this will be 11 and above 3 will be 3 by 11 What is it? 3 by 11, multiply by 33 means the answer is 9 Your things will be so simple Right? But the point is That we have to learn how to write this and remember it Now actually if you do 27.27 by 100, it will be 3 by 11, after simplifying Right?

Now let's try to understand this will be the first step to be faster. Okay. So now let's learn which percentages we can write in which ratio or fraction.

Okay. Come on. 10%. It is very easy to find any fraction.

10% means 10 by 100. This is 10%. How much is it? 1 by 10. How much is it? 1 by 10. Isn't it?

Meaning, 10% can be written as 1 by 10. 20% can be written as 2 by 10. Obviously, when you are going from here to here, it is 2 by 2, so do it by 2. When you are going from 10 to 30%, it is 3 by 3, so do it by 3. This is 3 by 10. Now it will be bright. If you want 40%, then think directly. 40 by 100, 4 by 10. Or think like this, 10 goes 4, so 1 by 10 goes 4, 4 by 10. Now you will know that this will be 5 by 10, this will be 6 by 10, this will be 7 by 10, this will be 8 by 10, and this will be 9 by 10. And it's not difficult for us to remember.

70% 7 by 10. 70 by 100. 1010. Where you face problems, pause the video. Remove the percentage sign from yourself. Upon 100, you will start seeing. Okay? Now, when 50% 5 by 10 means half.

Right? What was 50%, son? Half. 5 by 10 was there. What was 50%, son?

5 by 10, which I can simplify a little more and write 1 by 2 also. 50% 5 by 10 means half. If 50% is half, then what will be 25%?

Think and tell me, son. If you have written 50% and 25%, you have done half. So, this half will also become half.

And if you do half, then how much will be 1 by 4? You are doing half-half. This too you have done upon 2, this too you have done upon 1 or 2, then it will become 4. Isn't it?

So, 25% is 1 by 4, half of half. So, you have 1 by 4. Now, once you have this, you can move on. In fact, you know that 25% is a quarter.

Right? 1 by 4. From 25, I am going here, it is multiplied by 3. So, if you go here, what will happen? Multiply by 3, it will become 3 by 4. This will be brilliant, son. Look, son. From here, you went here.

How much did you multiply by 3? So, from here, what will happen? Multiply by 3. Similarly, Go from here to here.

What are you doing? This is 75.5. So, if you go from here to here, what will happen? This will be 1 by 2. What will be 3 by 4? 3 by 8. When you do half, the denominator will keep multiplying.

When you do 2, the denominator will keep multiplying. Say, 25% is 1 by 2, 12.5. 1 by 4 is 1 by 8. If you do half, the denominator will multiply.

Now, these are something which you can remember. You can do it. It is not difficult. Look and understand it well.

Take your time and pause. See, what is happening? 50% is half, you can see.

25% was 1 by 4. 12.5% was 1 by 8. Similarly, we did for 75 and 37.5. Now see, how can we remember this one? 1 by 7 is 14.28%. See, 7 becomes 14, 14 becomes 28. That's how you remember it. 7 to the 14, 14 to the 28, 14.28% is 1 by 7. 14.28 is 7.14.

Right? 1 by 7 is 1 by 14. Initially, it will be a little challenging for you to remember, but you will have to remember. Because with this, all these questions will end up in the air, as you saw.

Tomorrow, you will tell me 14.28% of 42. Instead of this, what will I write? 1 by 7. 1 by 7 multiplied by 42. 7 to 42 is a 6 answer. Is it shining or not?

That's why we are learning. Because tomorrow when you will be in classes, our regular one, your teacher will write 14.28% as 1 by 7. It will be written in solutions as 1 by 7. If you will multiply 42, you will say, Sir, from where did this come? Now that is why you need to know that 14.28% is 1 by 7. This will be cut. Here, 6 is written directly. And now you are two steps ahead from your fellow mates.

The method of memorizing is easy. The 10% line is very easy. It is getting by 100. This story is easy. If 50 is half, then learn from 25, 1 by 4. 14.28, 7 is the table. Remember 1 by 7. 7 to the 14, 14 to the 28. Go ahead.

Now, look at these two. Can you see any pattern? Yes sir. This table of 11 is not working. 11, 22, 33, 44, 55, 66, 77, 88. And you have done the same work.

You have put 0.B11 in front of 11. 0.B22 in front of 22. 0.B33 in front of 33. And this 9 table is working. 9, 18, 27, 36, 45, 54, 63, 72, 81. Isn't it? And you have put the same table here. 0.18 with 18. Did you see? This is the 11 table.

This is the 9 table. Criss-cross it. So, whose table was this? This table was 11. So, write 9 below.

Where 11 table will come, write 9 below. Where 11 table will come, what will you write below? 9. That's how you remember it. 11 table means 9 below.

I got it right. And where 9 table, when 11 table takes 9, so 9 table will take 11. What will everyone have below? 11, simple, you can remember it, straight forward, Sir, what is the numerator?

This is fine, if it was 11, then 9 came down, if it was 9, then 11 came down, Brother and brother interchanged between themselves. Now, if this 11 was 1, then write 1 here, if this 11 was 2, then write 2 here, if this was the third multiple of 11, then 3, if this was the fourth multiple of 11, then 4, 5th multiple is 5, 6th multiple is 6, 7th multiple is 7, 8th multiple is 8. These were the multiples of 9. So, which were the 9's? So, 9 x 1 is 9, 9 x 2 is 18, 9 x 3 is 27, 9 x 4 is 36, 9 x 5 is 45, 9 x 6 is 54, 9 x 7 is 63, 9 x 8 is 72, 9 x 9 is 81, and 9 x 10 is 90. Now, think how easy it is for us. Yesterday, he gave us a question like this.

How? 45.45% of 1111. Now the kid will go crazy. He will say, what nonsense is this?

45.45 upon 100 into 1111. I want a calculator. No. Whose is this multiple?

9. If it is 9's multiple, then what will come down? 11. Which is 9's multiple? 5th.

So you will write 5 of, means 1, into 1111. How much will it be? 11 becomes 0, becomes 1. 101 into 5, how much is it? 505. The answer is also there, son.

You are done. That's how your competitor, your fellow student is faster than you. Because he knows certain tricks which might you are missing. Right? Done?

Let's see the last one. 33.33%, son. If you do it by into 3, you will understand. If you do it by into 3, 99.99, close to 100. So, what can be written to it, son?

It can be written as 1 by 3. Is it 1 by 3? In fact, you will see it here also. It was 3 by 9. 1 goes, 3 goes. So, how much is it? 1 by 3. This half of this, how much is it?

1 by 6. Then, this half of this, 16.6, this half of this, 8.33. This half of this, 1 by 12. Now, the cat sometimes asks you this one. 37.5 and 8.33.

I have seen this multiple times. Right, this is mostly in simple interest and comfort interest because this type of rates can be there. 8.33 Of course, when CAT question comes, it gives a little bit relevant numbers.

So, the interest of any bank cannot be that it is giving 25% interest, 30% But it is around 8.33 And sometimes it is around 7.14% interest. That number is given so that you can use 1 by 14. So that whoever knows, can play the game well. So, I hope Guys, the story is clear till here.

Right? Now, let's see how we can use them. So, it's your turn. Do this question and show.

And now, you know that. Pause and try. See how fast it will be. What is 14.28%?

Sir, 1 by 7. Off means multiply. 37.5? Remember. What was 75?

3 by 4. It's half. That means 3 by 8. 75 is not caught, then 50 half, 25 1 by 4, right, 25 1 by 4, 12.5 1 by 8, and this 12.5 3 goes, i.e. 3 by 8, off means multiply, 112, question is over. 7, 8 goes 56, 56 goes 2, 3, 2 goes 6, answer is clear, that is it.

So, guys, it is important that you understand that how these percentages can be absolutely converted into ratios. OK, let's go. Let's look at this question.

Right, let's look at the problem. Now we will make a flow chart and finish the game. In a city of 27000 people.

Okay, there were 27000 people. Slowly, slowly, do it with me, by pausing the video and reading each line. 33.33% For you, this is not there.

What is going on in your mind? 1 by 3 I have kept it in mind. If you don't remember now, then write the table I made in the back.

Keep it in front of you. Do it by looking at it now. 33.33% For me, it is 1 third. Of the people age more than 40. So, how much is 40 plus? In my mind, it is 33.33%, which is one third.

One third of how much? 27,000. It will be overly.

How much will you do one third of 27,000? How much will it be? 9,000.

9,000 is over. Now, either you write it here itself into 27,000. But I am teaching you this so that you can do it in your mind. So, then all this will be in your mind. Right?

And 44.44% is clear in our mind. What is the multiple of 11? So what will come down?

9. Remember to turn the other side. 11's fourth multiple will come up to 4 by 9. Now multiply 4 by 9 with this. Into 27000. So how much is 4 by 9? 9 is 3. 3000. 3 into 4 is 12000. So our 12000 people are less than 25. Understood?

This is the end. Number of people that range from 25 to 40. 25 to 40 people will easily get out. 40 is above 9000. 25 to 12. How many did we get? 21. Total was 27. How many were left? 6000. Out of 27, 21 were left.

6000. 6000 were left in that range. But how could we do this question quickly? Because we knew that this is nothing but 1 by 3. We knew this is nothing but... 4 by 9. If we know that, we are faster. And we can do more questions on the day of exam.

Isn't it? Chala jaye. Alright.

Aajao beda ispe. Ab ye tumhara. Ek bar pause karo. Try karo.

Main hat jaata hoon. Screen se. Try it out.

Wapas. Normal sa flow chart and game khatam. Theek hai?

Normal sa flow chart and game khatam. Main maan raha ho apne question padh liya. So in a class of 99 students. Aajao wapas. 99 students.

22.22% of students are in red house. Okay. Take out red house students from here. How much is it?

22.22%. You know. 11's multiple will come down to 9. 11's second multiple will come up to 2. 2 by 9 into 99. 9, 11. 11, 2, 22. Red house students are done. 22 is over.

Done. Move forward. 27.27% of the students. Okay.

Which house is this? Yellow. So, let's write yellow.

Now, you know the fraction of this. What is 27? Multiple of 9. What will be the multiple of 9 below?

11. What is 9 3? So, write 3. Now, 11 will be 9. 9 3 will be 27. 27 will be yellow. Right. Read further. 50% of the remaining students.

Now, take care of this. Remaining. Isn't 50% total? 22.22% of the total students.

Students means total students. 27.27% of students means total students. But 50% of the students didn't write.

What did they write? Remaining. So if you write 50% of 19, then everything is ruined. Everything is hard work. 50% of the remaining students.

So first make a chain of the story. Now tell me how many remaining students were left. After that, it is important for them to have 50%. Don't do 50% of 99. No, no, no, no, no, no. 99% of 50% of remaining.

So first find out the remaining. 99, 27, 22, how much is it? This is 20, 20, 40, 49 is over.

49 out of 99 is left. How much is left? 50 is remaining. 50 students. Now talk.

So these remaining students who were 50, 50% of that is half. Which house have these 25 kids? They are in Green House. So, be careful with the remaining. All the questions in CAT will be brought in the picture.

We have to remember that whenever we talk about the remaining, we will first make a separate chain. We will first take out the remaining kids separately. After that, the story will run separately in a separate line.

Now come ahead. They are in Green House. then find the number of students in blue house. So, okay, I am not telling anything, so we have to assume that there are only 4 houses.

Right, so this is red, yellow, green, the remaining is blue house. How many are there in blue house? Obviously, 20. Clear?

25 A.B.Tick. Game is over. I will move once. You see the solution. Read the question.

And notice that how I am doing only by making flowchart. No equations. Nothing.

One flowchart is going in ratios from our percentage and in one time I am finishing the work. It is going on. Is it clear?

Right. Come on. We will take care of remaining. As remaining, flowchart will move forward. Remove remaining and start again from that.

Come on. Now let's become a little faster. Question is, what is 20% of 40? You know one.

You said, I will write 20% as 2 by 10. You just taught me. 20 by 100 will remain. You will cut 0 one by one. It will become 2 by 10. We are doing into 40. Right.

So, one is that I will write its fraction as 2 by 10. Due to which, it will become 4 and 8. Right. But, I have one more faster way. Listen to that.

Okay. One more faster way. Listen to that.

This method will work till then. First, you have learned the ratio. There is a way to calculate the percentage of 0s. Imagine what is written in 20%?

20 by 100. So, when you have a percentage of 0s, it is written in the last. For example, what is written in 40%? 40 by 100. What is written in 50%? 50 by 100. So, everyone has 0s.

Even 20 had 0s. So, 1 0 is not going to be deducted. So, I can't catch it anywhere like this, 4 by 10, 5 by 10, 6 by 10, 7 by 10. And I know what it means, 0.4.

What it means, 0.5. What is 60% going to be, 0.6. What is 20% going to be, 0.2.

If I had written it like this in my mind, 0.2 multiplied by 40, I couldn't write 8 directly. Because then it would have been fine for me to remove its point, it cut 0, 2, 4, go 8. That means, what would I have written 20% into 40? 2, 4, go 8, 1, 0, 1, 0. This 2, 0, 100 would have taken.

Isn't it? How much will be below percent? 2 zeros, 1 zero, take this 1 zero, this is left, 2, 4, 8. If the matter is clear, then look at it again. 30% of 4100. Will 100 come below percent? These 2 zeros must be finished.

Let's subtract 1, 1, 1, 2 zeros are finished. What will be left? 3 into 410. Sir, where are these 2 zeros? Take the 2 zeros of percent.

Remove this from mind. So, subtract 3 into 410. How much is it? 1, 2, 3, 0, finished answer.

Nothing is written. Try one more. 40% of 42, 1 zero. 1 zero is left, now keep in mind. Right, there are no 2 zeros, there were 2 zeros every time, we were cutting.

Here also, 2 zeros are cut, cut, 2, 4, 8, answer is there. Now, it's okay, you will keep in mind that 1 zero is left. 4 into 42, how much is it?

4, 2, 8, 4, 4, 16. But 1 zero is left, of the bottom. Put a point, what difference does it make? 168 by 10 is there, 1 zero is left, put a point.

That means multiply by 0.4, multiply by 0.3. Point. multiply by 0.2 multiply by 0.6 in 60% if it is 0 then the point will die and if it is not 0 then you multiply it and drag a decimal behind do you understand or not? here I multiplied by 0.2 here it was 0 I removed 0 from the point 2,4,8 here I multiplied by 0.3 it was 0 removed it 3x410 here I multiplied by 0.4 it was not 0 I multiplied by 4 168 came and dragged the point behind here I said I have to multiply by 0.1 I multiplied by 0.1, so 3.3 is here.

Or I multiplied by 1, so 33 is here. And I pulled one point back. Isn't it? Because only 1 zero was cut. 1 zero is left.

So, think however you want. But you can do it quite faster. Meaning, if you are told 30% of 42. Do 3x42.

3x6, 3x4 is 12. 1 zero is cut. The point of 3 is left. Put it here.

Understood? When you multiply by 0.3, you still have a point. Similarly, if we talk about 20% of 810, how do you multiply it? By 0.2. How much is multiplied by 2?

1620. There is a point left, isn't it? Let's put it here. Or think of upon 100 and divide 0 by 0. You can do 81 x 162. Then also 162 will come. If you do the point behind, then also it will come.

But you have to be faster. If you understood, then this one is yours. 40% of, let us say, 22. With whom do we have to multiply?

First, we have to multiply it by 4. 1 0, 1 0 will be eaten, the remaining 1 0, which will be given as a point. Or 0.4 into 22, which is 8.8. So, this has to be done in one line. Is it clear?

I will do one more for you. 30% of 12. 12, 3, 36. 1, 0, 1, 0 is over. 1, 0 is left.

That will be the point. Right? Or, it is 0.3, 0.3 into 12. 12, 3, 36. 0.3 was there. 1 point came back. No matter how you think.

If you are good in decimal, think from decimal. If you want to divide by 10, think from that. It is the same thing. But, you have to do it so fast.

Come on. 1, you start quickly. I will show you all four. Then, I will write together. This is for your homework.

Okay? Take your time. Come and tell me the answers.

I will know that you have caught it. Do it with shortcuts. Look, in my mind, multiple ways work. Either I will multiply from 0.3 to 0.4.

Or I will think that there is a 100 below. Both 0s will be finished. 3, 4, 0, 12 answer.

Right? Now, when you don't do 0s, then I will multiply from 0.1. If you do it from 1, it will be 45. If you do it from 0.1, it will be 4.5. What should I do with 15%? Mind your own business, son.

You will think of 10% of 42 plus 5% of 42. Isn't it? 15% is done. It is very easy to get 10%.

Pull one back. 4.2 is done. Isn't it? 1.0 will be deducted from 0.1.

Now if 10% is 4.2, then how much will be 5%? Obviously 2.1. Brother, 10% of something and 5% of something will not have any relation. Absolutely it will.

You have increased the percentage. The number will also increase. Isn't it? So, 4.2 plus 2.1 is 6.3.

That's it. Done. Now, you can also solve 35 like this. How can you solve it?

30% plus 5%. Right? Whose is to be done?

Of course, of 42. Of 42. 30% means to multiply from 0.3. You can do it from 3. How much is 3? 3 to the 6. 3 to the 4. 12. How much do you want to do?

From 3? No, from 0.3. This came from 0.3.

5% now, try to use it more. How much is 10%? 4.2. Right?

How much is 5%? 4.2 means 2.1. This is it.

14. Now, if you understood all this, perfect. And if it didn't come, then go back and learn this shortcut. Because this is going to make you faster.

And these short curves are not limited only to percentage. You will use these in profit loss, simple interest, compound trust. So we have to get our hands on these kind of percentage quick calculations.

Yes, you will have calculator in CAD exam, on screen calculator. But again that will take time in such small calculations. We can rely on our mind. Right?

Let's talk about percentage increase degrees and then we will do questions. Okay? Let's assume The question is, if 50 to 75 is the number, what percentage is the increase and what percentage is the decrease? Simple thing. How much did you gain by going from 50 to 75?

Obviously, when you jumped from here to here, you gained 25. What was the percentage? What was the gain of 25? How much was it?

It was at 50. You have to always take the base below. 25 is increased at 50. 25 is increased at 50. So, 25 by 50 into 100. 52 ja, that means you have increased by 50%. Bas. Abhi haan pe apka number chota ho raha hai, to degrees ho raha hai.

Kitna chota ho raha hai? Aap 10 se neechay chale gayo. 10 se neechay chale gayo, the kitte pe? 30 pe to.

10 by 30 into 100. And now see your trick come into picture. 1 by 3. 1 by 3 kitna hota tha beta? 33.33% ki to baat ho raha hai. Done. And this time this is decrease.

Clear? So, this is your story. Percentage increase decrease.

Multiplying factors when you are talking about 10% of something, 50% of something, 30% of something. When you have ratios, you get 14.28%, right? 45.45% and all these things.

Let's go ahead and let's see how to assume a number. Now the rest of the things are easy. Here till the base, which is a little typical for children, because it is new.

So I hope you have understood till here. If you have any problem in the back area, go back, watch the recording again and then proceed from here. Because now we are going to attempt some problem sums. So fix the back one, set your hands, do all the questions I have done, try them once yourself. Right.

Then see my solution and then check. Right. Now see. You will get a question like this. Read the question and pause it.

Now this question is very common. The question is, Mr. Rahul gave 30% to Mr. Rora, 50% of the remaining to Mr. Vineet. Mr. Rahul invested the money left with him in a scheme which doubles the money in one year.

Find by what percentage the money increased or decreased for Mr. Rahul in entire transaction. Now, in front of the child, a question like this comes in the paper. We have to understand it and do it in two minutes.

We have to accept that when the question comes in CAT, multiple scenarios are happening. And we get scared there because we haven't learned to read the question. We run to make a question. Let's assume that Mr. Rahul has X rupees. Then, if he is giving 30%, then 30% of X.

and make such big equations. No. When everything is about percentage or ratio, that they had something, gave some percentage, gave some percentage of that, while doing something, it doubled.

Everything is in ratio. And then in the last, how much percentage degrees, they finally ask you the percentage. You will take a number and end the game. How?

Let's see. First, read this question line by line. Just read this much. Mr. Rahul gave 30% to Mr. Rohra and 50% of the remaining to Mr. Vineet.

Okay, so let's assume that Mr. Rahul had 100 rupees. Right? Now see how easy it will be. 30% to Mr. Rohra.

The advantage of assuming 100 is that you gave 30% to 100, so 30 to whom? To our Rohra sir. So what's left? You have 70. What's this? Remaining.

Right? You must have understood that cat will play remaining a lot. Right? So this work is done. We are a step ahead from the question.

The first step of the question is over. Right? Just remember that you have to assume that the one that Rahul ji brought, how much did he bring?

He brought 100 rupees in the starting. 50% of the remaining, not 50% of total, of the remaining. How much was remaining?

70. Who will get this? Vineet sir. 50% of this is half of this.

Half of this means that Mr. Vineet Sir has got Rs. 35 more. So we have resolved the first line. 30 is given to Mr. Dora Sir, remaining 70. Half of 70 means that Mr. Vineet Sir has got 35. Now the remaining 35 is left. This is the remaining left over.

Now let's go to the next line. Mr. Rahul invested the money left with him. Which 35 is left? in a scheme which doubles the money in one year. So, after one year, this money doubled into 2 and today it has become 70 rupees.

So, rather than making equations, when you understand all these things and try them yourself, you will see how fast it will be. When the class started, I was solving something. That was the question. And there you will see how I was just writing lines. I didn't have to make a chart.

But that will take time. First, let's make a chart and learn so that everything is clear and the notes are good. Right? Two lines have been solved.

We had brought 100 rupees. We had accepted this. This was our assumption.

Which we know is going to help us rather than making an equation. 30 Rora sir got 30%. 50% of the remaining. Remaining was 70. His 50% was 35. Vineet sir got it.

The remaining 35. Remaining. He put it in the scheme. Rahul ji.

And it doubled. And it became 70 rupees. Right?

Now he is asking, tell me, how much percentage did his money grow or decrease? He started with 100. After all transactions, how much did Rahul Ji get? It doubled, so this is 70. So that means that Rahul Sir is from 100 to 70. The percentage has decreased.

How much did you go down? You went down from 30. That means 30% decrease has happened. Another benefit of considering 100. How much has decreased?

30. So if you do 30 by 100, the base is this. Into 100. If you cut 100 by 100, it will be 30%. That means when you consider 100, So, one more advantage is that if your 20 is less in the last, then 20% degrees.

If 12 is more in the last, then 12% increase. Whatever number is shifted from 100, that is the percentage itself. Why? Because what will you do?

You will write 30 by 100 into 100. This 100 will be cut, right? So, the advantage of counting 100 is that to get the percentage, you have to multiply from 100. Base is also 100. Game is over. 30% degrees.

This is your answer. So, a person. Rather than making equations, he is just writing 5-6 words and he is getting the answer.

Once he is doing the question on his own, he is not explaining to anyone. He is just laughing, remaining, Vinit, remaining. Rahul does not write this.

He ends the game directly. Just like I did on the first page. Now it's time for you to try this particular thing.

But take your time, pause it, look at it once, understand it, try it in 2-3 questions and show it. Question for you. Do it brother.

Chalo, main maan ke chal raha hoon ki aapne question solve kar liya. To question kera in 2018, 10% of the students left the class. 2019, 30% of the remaining students also left the class.

2020, each student brought another student find the net percentage. Notice karo, wapas saari ki saari baat percentage pya hoon. There is no such thing that 30 students came in a year.

These 25 students left. There is no fixed number. If this had happened, there would have been tension. But here everything is percentage.

10% went here, 20% more, 30% more, double, triple. Here you assume without hesitation. I assume and we will direct a little bit.

How many students do we have? 100 students. 10% of the students left. You know 10% of 100. 10% of 100 is 10. 10 students ran away. How many students are left?

90 remaining remaining a mess if I live home okay up guys over at 30% of the remaining students right I'm the bad girl 30% of the remaining a semen remaining a guy like so is cut 30% get the other point three right point is a multiple of a 30% a guy the point three into ninety seven a guy took it down in three 27 right or point yes kajal a guy over budget get the 63 So, we reached this line again, that 63 students are left and we only need 2 small tables. So, if we know multiplying factors and know how to convert into fractions, then the game becomes easy. So, I reached here by doing this.

First, 10% out of 100, that means 10 students left. 90 students are left. Because, what I am saying is, 30% of the remaining, if you miss this remaining, then everything is ruined.

Remaining is very important. Don't miss this word. So 10 ran away, 90 were remaining.

What is 30% of this? What is 30%? Multiply it by 0.3.

0.3 x 9, 0 is deducted from 0. 9 x 3 is 27. 27 ran away more, isn't it? How many are left? 90 minus 21, that is 63. Now, in 2020, every child went and brought another child.

So 63 children, 63 children must have brought more. Every child brought one. What is the net? 126. Now, what is the net percentage increase?

From 100, If you have reached 126, then you have increased it to 26. And 26 means 26%, 100 means 100, you know that. Done. Again a simple flow chart and you are done, absolutely done.

This is the power of flow chart. If you understand, then write it once that yes sir understood. I will understand that you have understood, right? And if you still have a little doubt in this, then go back.

Try both the questions again. See what is happening again and it will be absolutely clear to you guys. Okay? Let's do one more question.

You answer this. Okay? Pause and try again. I will leave now. Now we will assume the numbers properly.

And this time, that number will not be 100. Why it will not be? How did you know? That will also be understood.

Read the question first. Okay. I assume you have read the question.

In a school, a student can score grade A, B, C or D in a test. If 14.28% of the students got A grade, very good. 22.22% of the students got B grade, very good.

20% of the remaining got C. Remaining is brought, keep this in mind. Find the approximate overall percentage of students who got D grade.

Sir, we will assume that all are percentage. It is true, sir. It is necessary to assume. It is all about percentage. Assume is a must, no doubt.

But, if you have assumed 100, then see what happens. 14.28% of the students. Now what will I say that 14.28% of the students were in grade A? This will start getting tense, who will do this calculation? We were assuming because the numbers are good.

Now we have to do 100-14.28, will 22.22% of that be good or not? We will get stuck. I was not having any problem in life till now because if you notice in the questions at the back, I was not getting good numbers like 10%, 30%, 20%, 40% type numbers.

I will assume 100 and move on. Now see one thing, how do I assume the number well? Listen to me. 14.28% how much is it? Is there any strike in your mind after seeing this number?

You should do it. What is striking? Sir, 1 by 7 is striking.

This was 1 by 7. 22.22% is striking in your mind. Yes sir, this is 11's multiple. So, sir, 9 will come down. 11 goes 2, so 2 by 9 will come. So, I have come to know that I have two fractions written.

Taking out 14.28% means I have to multiply the number by 1 by 7. So, when I am assuming, if I assume 7's multiple, won't I get benefit? Means, when I was assuming 100, and its 14.28% means 1 by 7 multiplied so 1 by 7 into 100 was not a good thing but if I assume 70 instead of 100 then 14.28% would have been easily taken out in 1 by 7 of 70 When you know which percentage you have, and who you have to multiply, then you can put a number here that is less than 7. So that this number is good. And when I know that I have 7 and 9, I can handle this 20%.

When I have 7 in the denominator and 9 in the denominator, then I can put a number that is less than 7 and 9. What is the number that is less than 7 and 9? Multiply these two. 7 is 9, so 63. Now, I will assume the number 63 and my question will be easy.

But how did I think? I looked at the percentages. The denominator of the fractions of these percentages, listen carefully, the denominator of these percentages, when the fractions are written, the denominator that was being given, we have to assume the number that is deducted from that.

And the number that is deducted from 7 and 9 is 7 into 963. So today I will assume that my number was 63. Now when 14.28% of the students got A, 14.28% is 1 by 7. Multiply by 1 by 7. How much is it? 9. Easily got it now. So 9 got grade A. How much is 22.22%?

Sir, 11's multiple is 9. 11 to 2 means 2 by 9. Multiply by 9. 7 to 2. 14. What did you get out of 14? B. And 20% of the remaining.

So first go to remaining. How much will be remaining? 14 and 9, 23. Total 63. 63 minus 23, 40. 40 is remaining.

Now remaining 20%. 20% is to be multiplied by 0.2. Point will be deducted, 0 will be deducted. How much will be?

8. Right. That's why I am saying 20%, 14.28%. Which means 8 students got D grade. Point the approximate overall percentage of the students who got D grade. How many students got D grade?

8 students got D grade. So, 32 students got D grade. And, he is asking us how much percentage of students got D grade.

So, 32 students got D grade. So, 32 students got what percentage? Overall percentage.

So, overall students got 63. So, 32 by 63 is what percentage? Do it into 100 and get the answer. Sir, who will do this? Who will do 32 by 63?

What are you saying? Use your brain. Even if there are options, it's part of the question.

Can't I approximate? If it was 64, it would have become half. Would it have become or not?

And what would be half into 100? 50%. This would be very close to 50%.

So what is this option doing? This is not in the picture. No problem. It's very close to 50. Half is written almost.

But sir, all three were near 50. How can I find out? Think about it. Is this half bigger or smaller?

Obviously, half of 63 is 31.5. If it was 31.5, you would have got exactly half and 50%. This time, you are slightly bigger than 31.5.

That means the answer should be bigger than 50. What is the half of 63? 31.5. If it is more than 31.5, then it is more than 50%. And if you are below 31.5, then you are below 50%. You are more than 31.5, you should get more answers than 50%.

These two are below 50%. The answer is over. Use options. Yes, if there were 3-4 options above 50% and close by, then we would have been stuck.

Then we would have to pick up the calculator and do it. But still, this story happened so easily. Now, he was explaining it.

Otherwise, I would have explained it, I would have accepted Direct 63. Why? Once you understand these things, you will become faster. And if you try to go back the conventional approach again, yes.

It will be easier because you already know it. That is nothing new for you to learn. But you will be slow. And by the end of 7-8 months, when you will be near to CAT 2024, then you will realize that you should have learned it. So even if it takes time today, you have to see one method four times.

But learn it. Because it will not only help in percentage, but in the entire application of percentage. Which is simple interest, compound interest, profit and loss. Even mixtures. Okay?

Let's go guys. Now, jump to the third topic that is Assumption plus Unitary Method. Abhi tak aapke question ko jis tarike ke dikhte the.

Right, we did this question. See, isn't it? We did the same question. Rahul gave this, this, this, that, right? Everything was in percentage.

Now this time, there will be a slight change. What will be the change? He will remove this last line, right? And instead of the last line, he will do something else.

Like this. Here is the seam. But in the last line, instead of asking how much the net percentage has increased or decreased, he will say that Mr. Rahul is left with 1050 rupees. Now tell me how much he brought. Right?

Now let's understand how to do this. Don't be afraid. As soon as you see the question like this, Percentage, then percentage, then percentage.

Right? We will play the game. He was giving us the tension of 1050. The new one, we will see that later. You solve line by line. Let's again start the game.

Mr. Rahul gave, I will assume again. I will assume the same as before. One step will increase, nothing else.

What did I assume? That Rahul ji, he 100 rupees lekar aagay. So, ae baat hai.

30% yunne Rora ji ko diya. To Rora ji jo hamare hai, wo 30 rupees leke chale gaye. Remaining hamare paas baj gaye, 70 rupees.

Bohot bhiya. Shahbaz sir. 50% of the remaining mele Vineet sir ko. To Vineet sir jo hai, wo 35 leke chale gaye. Aur ab jo inke paas remaining baj gaye hai, left mai likh deta hu, wo ho gaya 35 rupees.

Ye to humne peechay giya. He invested it and it doubled. And today, Rahul has 70 rupees. Till here, there is no tension in his life.

We know to do assumption. This part of our question will be step 1. Which is called as assumption. This part is over. Now see how the unitary method will look. Now the question will be, Mr. Rahul is left with 1050 rupees.

How much money did he have in the beginning? Now listen to this carefully. There are two stories here.

One, which is our assumption story. One, which is our real story. Is that right? And two things are important for us.

One, how much money did Mr. Rahul have left after doing all the stories? That is, how much left money does he have after doing all the stories? And the second important story is, how much money does he have?

in the beginning. Why is this important? Because in the question, one of them is giving and the other one is asking.

These two will be important for me. One will give value and the other will ask. These two are important. We will match these two with the ratio and unitary method.

Now let's see which two quantities are important in the sentence. The one who is giving is left with after doing everything. The other one who is asking in the beginning. So I wrote both of them.

Is this a real scenario or an assumption scenario? What do we know? We know everything about assumptions. You can ask anything, but we know everything about assumptions. Let's look at it according to assumptions.

After doing everything according to assumptions, Rahul Ji had 70 rupees left. And how much was it in the beginning? 100. That means, its ratio is 70 by 100, 7 by 10. The ratio will not increase without increasing.

Now talk about real scenario. What do we know about real scenario? There were two things in real scenario. One will give and the other will ask.

So, the one who will give, he knows. What is given in this? 1, 0, 5, 0. In the real scenario, he is telling us that 1, 0, 5, 0 rupees. 1, 0, 5, 0 rupees.

In reality, he had saved it. Is it true or not? Clear? Done?

Now, finish the game. Now, finish the game. You have to get only one thing, the beginning one.

How will you finish it? This upon this is equal to this upon this. Bro, their ratio will remain the same. Everything is in percentage. If you had brought 100, then 70 would have been left in the last.

How many would have been brought? That 1050 would have been left. So this upon this equals to this upon this.

How did you do it? You know everything about assumption scenario. In real scenario, one thing will give a question. One thing will ask a question.

What did you give? How many are left in the last? What was he asking?

The beginning one. So these two quantities. entity considered given 1050 asking x assumption 70 left 100 this is your second part and this is the most important part this is your unitary method it will be solved easily see cut this 0 0 cut this 7 7 1 7 5 15 16 So, x will come here and this will go here.

Solve it easily, x will be 1500. I have a little space left, but you solve it. This 7, 15, 105, x here, 100 x 15, 1500. Take 1500 rupees and the game is over. The same scenario that you know, one thing is being added at the end, which one?

Comparing the entities. Which entities? One who is giving, the other who is asking. Use the unitary method, the game is over.

You will always know about assumptions, because you have resolved the whole scenario of assumptions. Here, one of the two is giving you, that's why the other is asking. Done. Do one question by yourself. I am keeping it at the back.

Pause it once. I am on the side. Done. Now this one is yours. Try it.

Okay. I am going to do it. Again the same scenario. There is a class.

Some 25, some percentage. I am not asking the percentage at the end. Last, I said find the number of students in the class if the number of students in the green house were 56. So, remove this line.

We will add this last when we have to apply the unitary method. First, you assume the question to be simplified and solve this much. Do the assumption part.

We will see the next part later. So, let's see the assumption part. In a class, a student has the option of choosing one of the four houses.

Very good. 30% 20% As long as it is 10's multiple percent, 100 people are not a problem. So, we said our class had 100 children. Alright, 30% of the class chose red. 30% how much is 30?

So, which 30 children do we have? Red house children. Very good sir. 20% of the remaining class has yellow. Okay.

Now, remaining is saying, son, we have to stop. If you write 2020 of this, everything will be over. Everything is wasted. Money is wasted. Right.

So, that means we have to wait. How much is remaining? 70 is remaining.

Now, let's run this story separately. We had 20% remaining. 20% of this means, multiply by 0.2.

Right? 0 will be deducted from 0. 2 times 7 is 14. How many of these 14 are there? Yellow house ones.

Okay. If the number of students who chose blue and green are equal, are the blue and green equal? So, how many are left? 14 out of 17, which is 56. And 56 is divided equally between blue and green. So, 28 is blue and 28 is green.

This is the end of your assumption part. Congratulations, you are 70% done. Now, 30% will come from the last line, which is your unitary method part.

So, get ready. Everything should be comfortable till here. Right? Now, let's see what he is giving us and what he is asking us.

This is confirmed. One will be our assumption scenario. One will be our real scenario.

Right? Now, one of these entities will ask us, and one of these entities will give us. Correct?

So, let's see what he is giving and what he is asking. Come on. Find the number of students in the class.

That means, what is asked is the number of students in the class. Right? So, one thing happened, the one who is asking us, that is the number of students. Now, if we talk about the number of students in the class, then we know in the assumption. How many did we consider?

100. How many in reality? We don't know, that's what he is asking. Now, what is he giving?

If the number of students in the green house, which one is it? Green house. How many are there in the real scenario of the green house?

56. According to our assumption, how many are there in the green house? 28. Are you done, son? You are done with the unitary method. Wait a minute. Now, here it is happening like this.

28 goes to 2, so 100 goes to 2, i.e. 200. Or if x goes here, it goes there, so x comes to us. Sometimes the directives are 2x2, so this will also be 2x2. 200 answers, you are done. It's that simple, guys.

Chart, 70%, 30%, unitary method, you are done. Take your time. I didn't know that I am green or number of friends. It's possible that I would have compared yellow if he would have given me given number.

Here, yellow is given. Same scenario, in fact, if you see, I can make 5 questions from this question. In fact, if you print a book, you guys sit and print a book. Keep changing this thing here and the book will keep on being made. 5 questions will be made like this.

Should I show you the rest? Yes, show me. Does the question look the same?

Read it. It's the same, sir. No.

From here to here, the story is the same. This time, the point is the number of students. I asked again the same thing, but the given thing changed.

If the difference between the number of students in Greenhouse and Redhouse was 6, that means, whatever change will come will only come in my unitary method. One scenario will be of assumption. One scenario will be of real.

What is it giving this time? Numbers, functions, greenhouse and red house's difference. Right?

Greenhouse and red house's. Difference, means the difference between green and red is given in 6 real scenarios. And it is asking the total students which is x. In the assumption part, you must have been champs till now. In fact, the question at the back is the same.

What was it? We had accepted 100 children. Out of 100, which one did we put 30 in? In red. Out of 70, how many children were left?

20% out of 70, means 14 children were left. They were in yellow, the remaining 56 were equal to green and blue, that is 28 and 28. This scenario is exactly the same as I gave you in the previous question. Now, the given thing was something else, maybe it was the children of green house.

Today, I am giving you the difference. So, let's see what is in our assumption. In our assumption, the total is 100. And the difference between green and red, number of students in green house and red house, see how much is it.

30 in red. Green by 28, how much is our difference? 2. This is as per assumption. 2 is going to go, 3 is going to go. So, how much will 100 go?

3 is going to go. So, x is 300. Game is over. So, if you can view that, fine, visualize it, fine. Otherwise, upon this, upon this, equate it. So, 3 is going to go, x is going to go there.

And this 100 is going to go there, x is 300. This is what you need to learn. Here, I am not going to make equations by taking x, y, z. This is what we have to learn, no equations, no.

You will solve such big 5 line questions, right? Now you will do it yourself. You will make a table and go there and solve it, isn't it?

Come on, son, this is yours. Out of the shirts produced in a factory, 15% was this, 20% interest was this. Remaining 88040 are left for the export then the number of shirts produced it.

So let's forget this part again. This part will be used in the unitary method. Solve the story till here.

Right? 15% and 20% are good, 100% will do the work. You start with your assumption that is you had 100. Pause after doing it.

And wherever you get stuck, play step by step. Not that your answer didn't match, then play it completely. No, step by step. As soon as you get the mistake, then stop and do it yourself. 15% means 15% is defected While 20% of the rest, rest means remaining If it gets messed up, then stop How much is rest?

85, your rest is 85 What is their account? 20% of the rest are sold in domestic So this rest is for sending them, domestic 20% means, tell me how much is it? Sir, multiply it by 0.2 Multiply 0.2 by 85, how much will it be?

170, 1 zero will be eaten, 17 will be left. 17 were in domestic. And what else did you do? You exported, obviously. So, out of 85, how much did 17 get?

Out of 75, 7, 68. 68, you exported. Correct. Assumption that the story is over.

Chain is over. If you have done it till here, then you have understood 70% of the story. You will do all the percentage questions. But you will not be able to apply the unitary method.

We will see that now. Right? Now read the remaining and see if the method is looking like a reunitary method. Check it.

Should I apply it? Let's go. Again, we have an assumption scenario. We have a real scenario. Let's see which quantities we have to see.

One will be given and one will be asking. Right? Let's go. Check it.

If the remaining 8840 Shirts are left for export. Which is the given quantity? 8840. Export ones are giving us.

How much is the export according to real? 8840. According to us, how much is the export? 68. Alright, very nice. Go ahead, Gani.

Then the number of shirts produced, which is the total. The total is asking which is X. According to us, the total is 100. Finish the game, guys. We will have to beat them, but the answer will come.

Cut a bit according to yourself. I will cut it. Okay. I will help you.

So, this upon this equals to this upon this. It is going from 17. 17, 4. 17, 5. 85, 334, 520. 4, 130 will go. X will come here. Equals to 100 will go there.

1, 3, triple 0. If you have got the answer, congratulations. You have just done a CAT 2017 question right now in your very first class. If you could do it.

So these kind of questions are definitely going to be there. Direct CAD ka sawal. Sirf aur sirf ek chhoti si cheech pe. Kya?

Yeh. A good assumption. Make the scenario. Unitary method.

You are done. That's how you do the questions in 30 to 40 seconds. Believe me, once you have the habit, yeh sab likhne mein apko time nahi laga hai.

Toh main samjha raha hoon. Aap rukh rukh kar rahe hoon so it's taking time for you. But when you become a pro, these all the things are just very very quickly done in the exam. Right?

So, guys, today's class is over. I will explain you a small part of multiplying factor. Let's finish the game. So, if I say 10% more than 300, what does it mean? Let's understand.

It means that you have 300 and 10% more is added. So, whose plus 10% is added? 300's.

This is the meaning of this statement. Or you can say 300 is increased by 10%. This is also the same thing. 10% more than 300 means 300. This is it.

Plus 10% more. Whereas, if it was happening in this way, 10% more than instead of this, I would have written 10% of 300. This would have been a very different thing. What would this mean?

This would have been 0.1 or 10% multiplied by 300. That's it. This and this are very different. Right? 10% of 300 was just this. This has 300 already.

10% more has been added to that. Is it clear? So, 10% of 300 is a different story. 10% more than 300 is a different story.

So, this is 10% more than 300. Now, there are two options. Either you solve it. 300 plus 10% is 0.1. Multiply by 300. You have learnt this.

Now, you will take this 300 plus 30. And you get 330. So, one is this method. But we are not going to do this. Now, let's go to another angle.

If you take 300 as common, then what will be left? 1 will be left here. 10% will be left here.

What is 10%? 10% which is nothing but 0.1. You know what 10% is. 0.1.

Or you can see here, 0 to 0 will be 0.1. That is 1.1 into 300. This thing is called as multiplying factor. Now, see how useful this is. I have... This is all drama.

What was the meaning of 10% more than 300? 1.1 into 300 I could have directly written that. Think about it. 10% means 0.1300 has increased. 1.3 is already there.

0.1300 has increased. So, how much is it? 1.1 or not?

1.3 was already there. 0.1 of 300 is increased. So, how much is it?

1.1 That means, if you tell me tomorrow 20% more than n. I will say 1.2n. That's it. It is n. 20% means 0.2n has increased more.

Now 1 was there. 0.2n has increased more. 1.2 has increased. See.

1 plus 10%. What happens there? 1 plus 20%.

20% is 0.2. 1.2 does not happen. Similarly, if you tell me 35%.

More than n. So, it is 1. Plus how much are you getting? 35% which is nothing but 0.35. Meaning 1.35n. If you get it right, then it is very good.

You can solve all these equations like this. 10% more than 12. How much is it? Sir, 1 was there.

10% means 0.1 more. Meaning 1.1n. How much is 12? n is 12. How much is it? 11, 12 goes to 132. 1 decimal is 13.21.

Next, 20% more than means 1.2. 1 was there, it will add to 1. How much will it add? 20%. What is 20%? 0.2.

Add to 0.1, 1.2. Into 50. How much is it? 60. 70 is increased by 30%. That's the thing.

This means 30% more than 70. 70 is the same. 30% has increased more. That means how much? 1.3 times. Whose?

70. Point will be removed. Zero will be removed. 13, 7, 9, 11. 20 is increased by 26%.

That means again, 26% is increased. Who is 20? 26% is increased.

That means 1.26 into 20. Now, multiply it by 2. How much is it? 252. 1 is 0. 1 is a point. 1 will increase. Then also, 1 point will remain. 25.2.

Game over. Done. That's how you will finish all these things if it talks about percentage increase and degrees as well. That's all you have to do.

If you understand this, then degrees are very easy. Same thing, what does 10% less than 300 mean? Something has gone from 300. How much?

10% of 300. Means, if 300 is common, then the first one which was being added, is being minus 10%. And 10%, you know, is nothing else. It is 0.1, which becomes 0.9 into 300 now. Now, I would have written directly from here.

Means, if you tell me 20% more than n, then I will write 0.2 into 1. add and what I say in mind is 1.2n. This happens in my mind. Now if you say 20% less than n, then I do 20% out of 1, which means 0.2 minus, which becomes 0.8n automatically in my mind. So if you increase 30%, then 1.3, if you decrease 30%, then 0.3 out of 1, which means 0.7 is left. The story will run from 1. If you increase, then I will increase from 1. If you reduce it, then I will reduce it from 1 because it was that much.

I had brought 300. According to that, I went up or down, so 1 300 is there. Right? Clear?

See it once comfortably, it will be done. Then apply it after that. 10% less means, 1 was there. 1 minus 10% is how much?

0.1. Will this happen in my mind next time? I did it for the first one.

1 minus 0.1, 0.9 into 12. How much is it? 108, 1 decimal is 10.8. 20% less than 50, how much is it? If we did 20%, then we have 0.8 left. From 1, we have 0.2.

Into 50, how much is it? 40. 70 is decreased by 30%. That's the thing, that 30% is less.

If 30% is less, then how much is it? 0.7 is left. If it was more, then it would have been 1.3.

Into 70 equals to 49. I'm leaving the last one for you. Do it and let me know in the comments. Yes, sir, we learned. It was fun. We broke a lot today.

Now this increased degree will help you a lot in the application when I will bring the next lectures. SICI Profit and Loss. How to get a certificate in percentage? Watch. Question will be made in one line.

Game over. Always study line by line. The whole question never increases together.

I scored 40 marks. After review, every marks were increased by 40%. If something increases by 40%, then what is multiplied by?

1.4 multiplying factor. This is the multiplying factor that you multiply. 1.4.

Son, there was 1. If you are increasing, then move forward. How much to move forward? 40% means 0.4.

How much to move forward from 1 to 0.4? 1.4. If you take 40% back, then 0.4 has to go back. From 1 to 0.4, it went back 0.6. That's it.

So now that's it. First it was 40, 40% increased. Even after that, it failed with 4 numbers.

How many have it come? It has come 56. And still it has failed with 4 numbers. So if it had come 4 more, then it would have passed.

That is, 60 have become your passing marks. Game kata. Itna simple ho jayega.

Question bus dekhne me difficult hai. But if you know the multiplying factor, percentage ka game kata hai. Agar mai apko ek quick revision do, to humne jo aaj mota mata sika. Ek to aapne sika ki percentage ko fraction me kaise leke jate. Wo aapko yaad hain nahi hai table.

Right. Doosra jo main mudda aapne sika hai. That is 20% of 40 ki baat karo. So this is 0.2 multiply by 40. Which is nothing but. If you do 240, it will be 80 and it will take 1 point decimal.

One thing is 20% more than 40, which is 20% more. 0.8 in 1 means 1.2 into 40, which is 48. And another thing is 20% less than 40. Now, if 0.2 goes from 1, then how much will be left? 0.8.

Decimal will be this, 84032 will be taken. right. Then you have understood how to assume plus how to apply unitary method.

Done. So, guys, this is it. So, this is the start to a new revolution, where you do not have to be afraid even if you are a newbie to quant. You understand that yes.

It's not going to test you on higher mathematics. It's going to test you on the basic things which you also know. So if you think that only IIT and C can score, or only engineers can score well, or only those who have prepared for a competition can score well, then you are wrong.

Because the concept is the same which everyone knows. It's just that because they have prepared for any competitive exam, so it's a little fast. They have the other approaches.

We are going with the same traditional approaches which we had learned in our childhood. Which one? Accepting X, accepting the equation.

but the game is not there. So, rather than assuming x, y, z and making equations and spending time, right and giving a chance to you know big equations can also lead to sometimes silly mistakes. We are going to apply such approaches and be faster. So, before you start your preparation, understand that it is a game of aptitude. And we will use such scenarios and such approaches in life classes.

So, if you already know them, then you will start on the same line. Whether it is an IITian, a commerce student, an average student, a good student or a mediocre student or even less than mediocre student. So, once you have all the same line, then there is no excuse to ask for.

You have all the time. revise all these things, see all these approaches which you might take in the classes. So that is it for today. This is your quant mentor Rahul Bhatla signing off and let's continue this revolution with the upcoming classes.

Take care. Bye bye and have a great day.

Transcript for:Mastering Quantitative Techniques for CAT

Transcript for:
Mastering Quantitative Techniques for CAT