Understanding Discounts and Calculations

Hi, welcome to a tutorial on discounts from careerright.com. Discounts has its base in percentages and is generally asked in combination with profit and loss in placement tests, job interviews and all other competitive exams. These exams have 1 to 2 sums of discounts. Today, we will learn how to pick solve all types of discount sums that may be asked in exam. You can practice discounts and other quantitative aptitude topics on careerright.com which has 1000 plus aptitude questions and practice test for you. So let's get started. Let's get started. Let us understand what is the meaning of discount. Now say this is a book and the price of the book is say rupees 250. If you are buying this book and say if the shopkeeper is giving you say 50 rupees off or 50 rupees discount. So what does that mean? That means you have to pay 50 rupees less. That means the price of the book now for you would be 250 minus. 50 equal to rupees 200 that so discount means paying less amount of money or giving less that is the meaning of discount generally discount is can be given or expressed in terms of absolute values like 50 100 etc or it most of the times like say in most of the sums discount is expressed in terms of percentage that is 10 percent 12 percent okay whenever you go out for shopping you will see that there is flat 50% off then there's up to 40% off and all this stuff so this off which is given flat 50% off or 40% off that is nothing but discount right so discount is nothing but paying less money so now if say if this is a book and if a person is giving 10% discount on this that means you have to pay 10% less amount of money so how much money you will actually pay that would be total percentage we have seen That is nothing but anything, any object which is there that is always taken as 100%. That entire object is 100%. Now price of the book is 250. So 250 price is nothing but 100%. Out of that discount is 10%. So minus 10%. So you will get 90%. So the price of the book now is 90%. So you will just have to pay 90% of 250 rupees. And that is nothing. but the price of the book for you. So whenever they have given discount it means that you just have to remove that percentage from the from 100% and that remaining thing is nothing but the price that you have to pay. Now there are some terms which are very important and are related to discount. Let us see what the terms are. The first term is marked price. See on the left hand side corner marked price. Second is list. price. Third is advertised price. Okay. Advertised price. All these three things mean the same. Now let us see what these three things mean. Let us say on the over here we have our book. Okay. Price of the book is 250 rupees. That is nothing but the marked price or list price or advertised price. This is the price which is written on the book. That is 250 rupees. On that the shopkeeper gives say 10 percent. discount okay so this is nothing but discount so how much now the book will cost now 10 of 250 what is 10 of 250 just put a decimal point so 10 is nothing but 25 rupees so 25 rupees is discount so now the price is 250 minus 25 that is 225 rupees this is nothing but the selling price of the book so shopkeeper will sell the book after discount will sell the book at this price 225. So what do what have we seen over here see at the right hand side bottom marked price is always greater than selling price. So marked price or list price or advertised price is always greater than selling price because we give a discount on marked price and then we subtract the discount and whatever is the remaining at that price we sell the book. So that is the selling price. So marked price is greater than selling price. So remember Remember this. Okay. Now, let's move on to another concept called as successive discounts. Many a times in exam you will come across a problem which says that a person got too successive discounts okay two successive discounts of say 10 percent and 5 percent. So what is the equivalent discount? Now what does successive discount means? For example if an object is of say 1000 rupees then the first discount would be 10 percent right then we will reduce this 10 percent from this 1000 rupees then we will get some price say it is A B C then again we we will give a discount of 5% on this price, this new price and then we get the final price. So, this is nothing but successive discounts. First discount, then the second discount. Now, instead of calculating it by this method, there is a very very simple and small formula or a tip we can call it. Tip we can call it to find equivalent discount. For example, if there are two discounts of 10%. and 5%. Then what is equivalent single discount? That means on combining these two, what exactly amount, what percent discount the person finally gets. So, single equivalent discount can be given by add minus multiply. by 100 whenever there are two discounts single equivalent discount of these two discounts is given by add minus multiply by 100 what is add add is nothing but add both the discounts 10 percent 5% minus multiply multiply means multiply both the discounts 10 into 5 upon 100 what we get over here 15 minus this is 50 upon 100 that is 1 by 2 that is 0.5 15 minus 0.5 is 14.5% so this is nothing but successive discounts this is the formula to find single equivalent discount instead of single equivalent discount of two separate discounts two successive discounts if there are three successive discounts we will find it out later on how to tackle that but if there are two successive discounts we can find the single equivalent discount in relation to these two successive discounts by this formula. What is the formula? Add minus multiply by 100. Add minus multiply by 100. Remember this 100 is under multiply. It is not under add. Okay. It is add minus multiply by 100. Add minus multiply by 100. Let's see some of the sums related to discounts. Question number one. During monsoon clearance sale, Amit buys a shirt at double discount of 20% and 10%. Okay. At what price he bought the shirt if marked price was Rs.1000 that means there was a shirt over here there was a shirt and there was a price tag that means marked price was Rs.1000. Amit got a double discount 20% and 10% that means he got successive discounts. And we want to find out at what price he bought the shirt. Now we can solve it in two ways. One is by the successive discount tip which we learnt earlier and one is by normal way. So in this way we can solve the problem. instead of solving by successive discount way, we will do it by the normal way because ahead we are going to use the successive discount tip. So let's now solve it by normal method. So price of the shirt is 1000 rupees. How much was the first discount? 20%. So what will be the price of the shirt now? 100% minus 20%. That would be 80% of the discount. marked price. Why? Because 20% discount has been subtracted out of the total price. 20% discount is subtracted. So what remains is just the 80%. So Amit has to pay now 80%. What is this 80% of marked price? Percentage means we know divide by 100 of his multiplication mark price is 1000. This is 10. So 800. So after giving 20% discount, the price of the shirt becomes. 800 rupees now take this 800 over here this is the new price right now again amit gets 10 percent discount on this 800 rupees right so what is the price now it would be 100 percent Minus 10% that is nothing but 90% of this new price that is 800 rupees. That would be 90 upon 100 into 800. This gets out so 720 rupees. So the final price at which Amit bought the shirt was 720 rupees. See how easy it was if we know the percentage discount. If you know the percentage discount, what we can do is we can simply subtract it and get directly the price of the shirt after discount. Or there is another way what you can do is 20% discount is there. So what is 20% of 1000 that is nothing but 20 upon 100 into 1000 that would be 200 rupees. That means discount is 200 rupees. So the new price is 1000 minus 200. 800 rupees same way now the price is 800 discount is 10 percent 10 percent of 800 is 80 right so now the new price or the final price which amit pays is 800 minus 80 rupees that would be rupees 720 both ways it is same okay this way or this way both it is same we get the same answer moving to question number two if successive discounts are 15 percent and 10 percent Then what is its single equivalent discount? Now what tip we have seen single equivalent discount of two successive discounts is nothing but add minus multiply divided by 100. So what it would be 15 plus 10 minus 15 into 10 divided by 100 that is 25 minus 10 10s are 1.5 that would be 23.5 percent right this is the single equivalent discount let us prove this that this is the single equivalent discount let's see how Let us assume the price is 100 rupees of an object. First discount is 15%. 15% discount is first. So what is the price now? That would be 100% minus 15%. That would be 85% of the original price. Original price. That is 85% of 100. That is rupees 85. So new price is 85. Now 85. rupees is the new price second discount given is 10 percent okay what is the final price 100 percent minus the 10 percent discount so the person has to pay 90 percent of the new price what is the new price 85 rupees so person has to pay 90 percent percentages divided by 100 of 85 rupees that is 90 into now this is nothing but 0.85 85 divided by 100 take this 10 take this 0 over here you will have 9 into 8.5 that would be 9 5s are 45 decimal 9 at 72 and for 76.5 so the person has to pay 76 rupees and 50 pesa right original price was 100 rupees the person is paying 76.5 rupees difference is rupees two 23.5 now 23.5 is nothing but the discount which the person has got right now 23.5 rupees is nothing but discount on the original price of rupees 100 so what is 23.5 how much percent is 23.5 of 100 very easy quantity 1 upon quantity 2 23.5 how much percent is 23.5 of 100 and since we want percent multiply by 100 what do we get 20. which is nothing but this which we calculated. So see here we showed instead of calculating such in a such a big manner, okay, such a big manner much better use this formula for finding successive discounts. It is very easy to remember you don't have to do anything just remember add minus multiply by 100 add minus multiply by 100 even if you repeat it 10 times you will be able to remember it immediately over here. Moving to question number 3. Question number three if successive discounts are 10% 20% and 30% Then what is its single equivalent discount now earlier? We saw two successive discounts now here We have three successive discounts what to do Do not worry again. This is very very easy to solve. Let us see how to do it. 10% 20% and 30% Okay, these are the three discounts first take. any two let us say i take 10 and 20 find the equivalent discount what is it equivalent discount is add minus multiply upon 100 what do we get 10 plus 20 minus 10 into 20 upon 100 what do we get over here 30 minus this is 200 upon 102 we get 28 percent right this is we write it over here year 28 percent equivalent discount of these two is 28 percent now take this take the third discount and find the equivalent what it would be add minus multiply divide by 100 so that would be nothing but 58 minus the zeros get cancelled we have 2.8 into 3 that would be 58 minus 8.4 that would be 49.6% this is the single equivalent discount in relation to the three successive discounts that we you that you get if there are four discounts say one two three and four what will you do find equivalent of this find equivalent of this and whatever the answer you get here and here find equivalent of this and you get the answer final answer or single equivalent discount see it is very easy just remember this small formula and you will be able to solve the sums moving Moving to question number 4. Two successive discounts with the first being 20% were given on a table having marked price of Rs. 6400. Finally, it was sold for Rs. 4608. How much was the second discount? Again, very easy. This can be solved in two ways. One by the successive discount formula and one by normal way. Let's solve it by the normal way instead of successive discount method. That is also easy. But let's go on with the normal way. Now the first discount is 20%. Do we know the second discount? No. Let us assume the second discount to be A%. What have they given? Marked price is 6400 rupees. 6400. The first discount given is 20%. Right. So what will be the price after discount? It would be 100% minus 20% discount. That would be 80% of the marked price or the original price. That would be 80%. upon 100 into 6400 okay what do we get over here 614 to 8 I shifted the 0 over here because it makes easier it makes the calculations easier we get 8 0 0 8 4s are 32 8 6 of 48 50 and 5 1 2 0 now this is the price after the first discount take that price over here now the price is 5 1 2 0 now the second discount that is given one is a percentage right so now what is the price that the person has to pay after a percent discount that would be 100 percent minus a percent right this is the price the person has to pay that is nothing but 100 minus a percent right 100 minus a percent is the price that the person has to pay after a percent discount and 100 minus a percent of the new price what is the new price 5 1 2 0 ok So what that would mean 100 minus A upon 100 because percentage sign is divided by 100 multiplied by 5120. This is the price which the person has to pay or the table is sold at after giving the second discount. Now but they have given that the table was sold for 4620. 46 sorry 08. 4608 rupees after giving two successive discounts. That means 4608 rupees is nothing but this price. Right. Right whatever we have found out it is nothing but this price over here. So let's calculate what do we get over here 100 minus a upon 100 would be equal to 5120. Okay, that would be 4608 divided by 5120. Now this looks like it is divisible by 2. So 2 2's are 4 4 1 2 2's are 4 11 2 5's are 10 6 2 5 6 0. So here we have 2. 3 0 4 okay now again this looks like it is divisible by 4 let us see what do we get 4 6 are 24 16 640 this is divisible by 4 4 5s are 37 26 5 76 6 this is divisible by 8 80 okay 8 into 80 8 7s are 16 2 so we get 72 upon 80 okay 8 10s are 8 9s are. So what do we have? Let's calculate it over here on the right hand side. We will have 100 minus a upon 100 would be equal to 9 upon 10 okay this goes over here 100 minus a okay this 100 minus a would be equal to 9 so a would be equal to uh 90 9 and 10 90 a would be equal to 10 percent so the second discount is nothing but 10 percent see how easily we got it in exam with practice you will be able to solve this sum in hardly say 30 to 40 seconds okay this is very very easy you just have to calculate It took time to calculate over here, but I calculated it to show you that these can get divided you will get better answers. You can be very quick at calculations and you will get the answer very very quickly. Now moving on to question number five. Sonali could not decide between discount of 30% or two successive discounts of 25% and 5% both given on shopping of rupees 2000. What is the difference between both the discounts now over here we will solve this by the successive discount tip which we have seen earlier what is it it is nothing but add minus multiple multiply divided by 100 right add minus multiply divided by 100 what have they given over here Sonali does a shopping of rupees 2000 she is given two choices she can either get 30% discount okay or she can have two successive discounts of say 25% and 5% right now she cannot decide between the two discounts what we have to find is the difference between both discounts right so let us see what to do now shopping is of 2000 first option is of 30 discount so how much is she saving or how much discount in rupees is she getting that is nothing but 30 percent of 2000 that would be 30 upon 100 into 2000 that would be 30 into 20 that would be rupees six 600. So in the first case Sonali is saving rupees 600. Sonali is getting a discount of rupees 600. Now let's see in second case we have two successive discounts. So what would be the single equivalent discount for both of them? Add 25 plus 5 by multiply 25 into 5 by 100. This is 4 5 by 4. So we will have 25 30 minus 5 by 4 that is 1.25 that is 28.75. percent right so she gets 28.75 percent discount in the second case so how much in rupees is she actually saving or getting the discount that is nothing but 28.75 percent of 2000 right that is nothing but 28.75 upon 100 into 2000 this gets cancelled we will get 28.75 75 into 20 so multiply by 2 what do we get 2 5s are 10 2 7 14 15 2 9 2 8s are 16 17 2 to the 4 5 multiplied by 10 that would be 575 rupees so in second case she gets discount of 575 rupees in the first case she gets discount of 600 rupees so what is the difference between both discounts 600 minus 575 that would be rupees 25. So the difference between both discounts is rupees 25. Moving on. Question number 6, which of the following will yield maximum discount on Rs. 6896? First is two successive discounts of 5% and 5%, second is single discount of 10%, third is two successive discounts of 8% and 2%. Now, you might think that this is pretty lengthy also the number given over here is looking a bit difficult and calculation will take time but no this is very very easy. Okay, let us see how to solve it. You know the formula for successive discount. that is nothing but add minus multiply by 100. Okay, and you just need to find out which of the following options will give you maximum discount. Now, say if you get a discount of 10% on one object and say 20% on the same object, then which of this option will give you maximum discount, but obvious this 20 is more than 10. So 20% discount means you'll get more discount than this same way over here, we need not consider the at all do not consider over here the amount just find single equivalent percentages of these and whichever percentage is higher that will give you maximum discount see how easy it was let's see the first option what is the first option two successive discounts of 5% and 5% so what is the single equivalent of this add minus multiply divided by 100 that would be 10 minus 2 or 25 upon 100 is 1 by 4 that is 0.25 that is 9.75 percent second one is very easy it is given single discount of 10 percent so it is 10 percent only third one two successive discounts of 8 percent and 2 percent what is the equivalent of this 8 plus 2 minus 8 into 2 by 100 10 minus 16 upon 100 okay now instead of calculating this we just want the max maximum discount no need to go into its calculation why 10 minus that means something is going to get subtracted from 10 is that right that means the value will be less than 10 we already have 10% over here right so this is nothing but largest okay amongst 9.75 10% and some value which is little bit less than 10 largest is nothing but 10 so this is the one this option will give you maximum discount See how easy it was in exam you will be able to solve this in hardly 15 seconds. 15, 10 to 15 seconds or sometimes always remember a small trick. Say if the percentage now over here is 10. 10%, single discount of 10%. Now these two successive discounts are 5% and 5%. If you add 5 plus 5 what you will get? You will get 10. If you add this 8 plus 2 what you will get? You will get 10. Whenever such options are there, always remember the single equivalent discount of 10% will always be there. always be greater than two successive discounts whose addition is 10. For example, let us say a discount is given of say 15%, single discount of 15%. This will always be greater than successive discount of 10% and 5% or say take any value 2% and 13% addition of these 10 and 5 is 15, 2 and 3 is 2 and 13 is 15. So, greater than this is nothing but single equivalent discount of 15%. You saw over here. 2 successive discounts equivalent discount came out to be 9.75 which is less than 10. Always remember single equivalent single discount not equivalent discount single discount is always greater than successive discounts of the same value. Now moving to question number 7. Raj decides to sell his watch at 5% discount. But his brother buys it from him and he gives his brother 8% discount. Due to this, Raj gets Rs. 45 less in profit. the marked price of the watch. Now, over here, what happens is that Raj wants to sell a watch. So let us assume that this is the watch. And the marked price for the watch is say, M rupees. Now Raj decides to sell the watch at 5% discount. But his brother is buying the watch. Because of which what happens to the brother? He gives 8% discount. That is 3% more. Plus 3%. 3%. Because of this what happens? Raj gets rupees 45 less in profit. What does that mean? The 3% discount which Raj gave on the marked price. 3% more discount which Raj gave on the marked price gives. him 45 rupees less that means this 3% on the mark price is nothing but 45 rupees had he given 5% discount only he would have got the same price as the previous one which he had decided but because of this 3% extra discount he gets 45 rupees less that means this 3% discount is 45 rupees that is 3% discount on mark price is rupees 45 so what we have to find is the mark price very easy 3 upon 100 because percentage sign is 100 multiplied by Marked price 45, 15. Marked price is Rs.1500. See how easy it was. Going to next question. Ramesh was getting two offers on a book having marked price Rs.800. Either two successive discounts of 20% each or two successive discounts of 30% and 10%. If Ramesh chose the better scheme how much more he must have saved compared to the other scheme again very very easy we know the formula for successive discounts add minus multiply by 100 okay what is the first option given to successive discounts of 20 percentage so equivalent discount would be 20 to plus 20 minus 20 into 20 by 100 that would be 5 this would be 4 so this would be 40 minus 4 equal to 36 percent what is the second option given 32 successive discounts of 30 and 10 so add minus 30 into 10 upon 100 that goes out to 40 minus 37 percent that means ramesh gets one percent more discount in the second case here it is 36 percent here it is 37 percent so ramesh chooses this scheme better scheme now they have asked how much more he must have saved compared to that other scheme that means when he chose the second scheme how much more did he save he saved one percent more why because 37 minus 36 percent is one percent so he saved one percent more now one percent which is there that has to be calculated in terms of rupees so that one percent saving is nothing but one percent of 800 rupees that would be equal to 1 upon 100 into 800 equal to rupees 8 so Ramesh says rupees 8 more while choosing the better scheme see how easy it was using the simple formula there was 25% off on handbags Madhu bought a handbag she also got a 10% discount for paying cash she paid rupees 405 what was the price tag on the handbag again very easy some let's see to solve it there were there was handbag there was 25% off on it okay we do not know the price of the handbag so let us assume the marked price be M rupees on that Madhu got 25% discount okay after deducting 25% she there was some price on that again she got 10% discount right and then she paid the final bill after these two discounts final bill was rupees 405 they have given 405 as the amount which she paid now what does this mean she got two successive discounts of 25% and 10% so what is the single equivalent discount of these two we know the formula for single equivalent discount add my add minus multiply upon 100 so what do we get we get 25 plus 10 minus 25 into 10 divided by 100 so that would be 35 minus 2.5 that would be 32.5% discount so madhu in total got 32.5 percent discount so what price did madhu pay she simply paid 100 percent minus the discount okay that is 67.5 percent amount so she paid 67.5 percent of what of the marked price right so she paid 67.5 percent of marked price but we already know that madhu paid 405 as the final bill so 67.5% of mark price is nothing but Rs. 405. So what would be the answer? Let's solve it. 67.5 upon 100 because percentage sign is divided by 100. Multiplied by M equal to 405. Let's divide by 5. We have 81 over here. We have 5 1's are. 5 3's are 15. 25 13.5 over here. Let's see if this is divisible by 3. Yes. 3 2's are 6. Then we'll have 21. 27 we get over here 3 4s are 12.5 4.5 okay again so we will have over here 4.5 into m is equal to 2700 right so again let's see whether this is divisible by 5 we get 0.9 over here we get 5 5s are 25 24 0 yes that would be m equal to 540 upon point point nine that is nine point ones are nine 60s are that would be 600 rupees 600 so the marked price is rupees 600 see how easy it was to calculate the answer moving to the next question question number 10 chandrika raised the price of their products by 40 percent how much discount should they give so as to sell the products on no profit no loss basis. Now, this looks a little bit tricky or complicated not much is given over here. But to solve such kind of sums, okay, let us use a very, very small tip or a trick that would make this very easy. Now in percentages, okay, this will make it very easy, right. So now in percentages, what we have seen is that whenever we do not know how to proceed, what we do, let us assume that the price of the product is rupees 100. Right? Now this will make it easier. Now they raise the price. price by 40% so price is increased by 40% more that means 40% of the original price that is 100 so rupees 40 more so price is increased by rupees 40 more so what is the new price new price is rupees 140 now new price is rupees 140 so do not consider the old price at all right now what are they what are they saying is that how How much discount should they give so as to sell the products on no profit no loss basis? Original price was 100 rupees. New price is 140 rupees. That means it is 40 rupees more. So if they want no profit no loss then they should reduce the price by 40 rupees. Is that right? Did you get it? If you reduce the price by 40 rupees and sell the product at 100 rupees you will be on no profit no loss basis. Right? So what to do now? So we know that Chandrika. should give a discount of rupees 40 right but we want this discount in the format of percentage so how to calculate how much is 40 percent of 140 why did we take 140 and why did we not take 100 because the new price is 140 now we should not consider 100 anywhere so how much is the discount 40 rupees of 140 we have learned in percentage quantity 1 divided by quantity 2 multiplied by 100 because we want percentage. So what do we get over here? 400 divided by 14 that would be 200 divided by 7 that would be 7 twos are 14 67 eights are 56 47.5% so approximately 28.5% discount has to be provided by Chandrika so that they give rupees 40 off and so that they'll sell the products on no. profit no loss basis see how easy it was I'll explain again 40% increase in price so the price becomes 140 if they want no profit no loss they have to reduce 40 rupees give the discount of 40 rupees so that original price again becomes 100 rupees but what is 40 rupees discount in terms of percentage 40 upon 140 into 100 why 140 because new price is 140 we should not consider old price now that gives out 28.5% discount. Thank you. Question number 11. There is a 10% discount on a dozen pairs of trousers marked at Rs. 8000. How many pairs of trousers can be bought with Rs. 2400? Very easy. Dozen pair of trousers means 12. 12 pairs of trousers. Cost of 12 pair of trousers is 8000 rupees. This is the marked price. Now there is a 10% discount if you buy 12 pair of trousers. 8000 rupees that would be 10 percent of 8000 rupees that is nothing but 800 rupees right 800 rupees is the discount so the final price now is rupees 7200 that is 8000 minus 800 right this is the final price now 12 pairs are bought for rupees 7200 so one pair of trouser is bought for 7200 divided by 12 that is rupees 600 Right? Now we have 2400 rupees with us. In 2400 rupees how many pair of trousers can be bought? One can be bought in 600. So in 2400, 2400 divided by 600 that would be 4 pair of trousers can be bought in rupees 2400. 4 pairs of trousers. This is the answer. Question number 12. Blackberry announced a discount of 25% on their trousers. Vivek went to shop. He He wanted to save rupees 400 in discount. How many trousers should he buy to do so? If each trouser costs rupees 320, cost of each trouser is 320, discount on each trouser is 25%. So how much is the discount in rupees? That is nothing but 25% of 320. That is 25 upon 100 into 320. 25 fours are rupees 80. So each trouser Vivek can save rupees. rupees 80. Now he wants to save 400 rupees in discount. Here in each trouser he is saving 80 rupees in discount. So how many trousers he should buy so that he will save 400 rupees in discount. Total rupees in discount he wants to save divided by amount of rupees he saves in one trouser. That would be 5 trousers. So if he buys 5 trousers he will save 80 rupees for first, second, third, fourth and fifth and this total is 100 rupees. So he will save total will give him Rs. 400 savings in discount. So he needs to buy 5 trousers. Question number 30. How much does the sarees sales revenue of Uday increase if Uday announces 25% discount on sarees and the saree sales volume increase by 40%? Again over here we do not know exactly how much is the revenue earlier, how much is the revenue later and all that stuff. So let us start by some assumption. Let us say that Uday sells say 10 sarees and price of each saree is rupees 100. So what is the revenue of Uday? Revenue of Uday is nothing but 100 rupees each saree into 10 sarees that is rupees 1000. This is the initial revenue of Uday. Now what does Uday do? Now Uday gives a 25% discount on sarees. So now initially the price was 100. 25% discount. Okay. So what will the price? 100% minus 25%. That would be 75% of 100. Right. That is nothing but rupees 75. This is the new price of saree. Right. Also they have given that the sales volume of saree increases by 40%. Initially Uday was selling 10 sarees. Okay. Now there is a 40% increase in the sale of sarees. In the number of sarees which are sold. So what is 40%? percent of 10 it is nothing but 4 correct so 4 is the 40 percent of 10 that means Uday is selling 10 plus 4 equal to 14 sarees now right this is the new volume right this is the new volume now what is the new revenue of Uday 75 rupees each saree into total number of sarees sold is 14 that is 1050 rupees this is the new revenue of Uday. So, what we have to find out is how much does the sarees sales revenue of Uday increase. So, new revenue is 1050, old revenue is 1000. So, the increase is rupees 50. 1050 minus 1000 that is increase is rupees 50. That is the rupees 50 increase. Now, if we have to calculate it into percentage, what we will see? We will take 50. How much percent increase is there if we have to find out? what we will do Take 50 divided by the new old revenue because we have to find out how much increase is there as compared to the old revenue right. So 50 upon 1000 into 100 since we want percentage. This gets cancelled this gets cancelled that is 5 percent increase in revenue. Moving on to question number 14. Question number 14. If a book costs Rs. 900 and is sold with a profit of 10% and discount of 12%, then the advertised price is... Now, this is a very easy sum. This might look complicated to you, but it is not. You just need some common logic over here that would be helpful to solve the sum. Let us see. There is a book. Now, there is some advertised price or marked price or list price to it. Let us say we do not know that price. We have to find it. Let us say M rupees is the advertised price of it, marked price of it. Now the book is sold at discount of 12%. So what is the price of the book at which it is sold? It will be 100% minus the discount of 12%. That would be 88% of the original price or 88% of the advertised price or the marked price. That is 88 M upon 100. So the book is sold for... 88M upon 100 rupees. Okay. Now, what have they given? The book costs rupees 900. So, the cost price of the book, that is the book at which the book is made is rupees 900. And it is sold with a profit of 10%. Now, let us say, let us take a very small example. Say, if you have an object. Okay. Price of it is rupees 100. And you want to sell it with a 10% profit. What you will do? You will take 10% of 100. 100 that would be rupees 10 and you will sell the book for your cost price plus this 10 rupees profit that is 110 rupees right so cost price is 100 and if you want 10 percent profit you sell it for 110 rupees let us see how 110 rupees converts to 10 percent profit 110 rupees is the selling price it is rupees 10 great rupees 10 greater than the cost price so the profit is rupees 10 is 10 and the cost price is 100 into 100 right that is nothing but the 10% profit right we know quantity how much more is the selling price than the cost price quantity 1 divided by quantity 2 and since we want it in percentage we multiply by 100 so 10% more so over here also cost price cost price is 900 rupees we want 10% profit right so what is 10% of 900 that is simply rupees 90. So the shopkeeper or the person who is selling the book, he has to sell the book at 900 plus 90 equal to rupees 990. Then only the person will get 10% profit while selling the book. Did you understand? It's very easy. Cost price is 900 and the person wants 10% profit while selling the book. So he has to sell the book at 900 rupees plus the 10% profit. That is nothing but 10% of 900 that is 90 rupees and hence the person has to sell the book for 990 rupees but we already know okay this is the price for which the books need to be sold okay book needs to be sold now we already know that the book should be sold at 88 M upon hundred and we also know that the book should be sold for rupees 990 that means these two values are equal so equating them what do we get 88 M you upon 100, 118 Zaar, 119 Zaar, 90 Zaar. So what do we get over here? We have 9000 divided by 8. That would be 8 1 Zaar. Again 8 1 Zaar, 8 28 2 Zaar, 48 5 Zaar. So rupees 1125 is the marked price of the book. next question. Question number 15. Profit of Raj while selling a book to Simran is Rs. 63. Despite a discount of 23% on the book, Raj manages to get 10% profit. What must be the list price of the book? Now this sum is very easy actually but you need to know one very small concept. It is very easy. It is related to profit and loss. This formula which I will be telling you right now. you will have to learn it when it comes to profit and loss because otherwise you won't be able to solve the sums right so the profit and loss formula which i am going to you it is like this percentage profit is nothing but profit in rupees okay profit in rupees divided by cost price multiplied by 100 so percentage profit is nothing but profit in rupees divided by cost price multiplied by 100 you have to learn this formula we'll see in detail about this formula in the profit and loss video but over here we need this concept because many sums related to discount are connected to profit and loss also. So let us see how using this formula will arrive at our answer. Now there is a book. Okay, there is a book and we do not which is sold by Raj to Simran now we do not know the list price of the book list by price means advertised price or marked price right marked price let us assume that the marked price of the list price is rupees M what have we learnt list price or the marked price is always greater than selling price and if you want to get a profit we know it is common sense selling price has to be greater than the cost price then only we will get profit otherwise we will have loss right just remember this it would be useful again when you you do profit and loss. Okay, now let the marked price be m rupees. Now Raj gives a discount of 23%. So how much would be the selling price of the book that would be 100%. That is the price of book minus 23% discount, that would be 77% of the original price, that means the marked price. So the book has to be sold at 77% of m that is rupees 77 divided by 100 multiplied. by M. So the book has to be sold at this price by Raj because he is giving 23% discount on the book. Now what have they given profit of Raj? Raj manages to get 10% profit right. This is 10% profit but they also say that profit of Raj while selling a book to Simran is Rs. 63. That means this 10% profit is nothing but Rs. 63 right. This 10% profit in rupees is nothing but Rs. 63. So, using this formula now, let us see what do we get? Percentage profit is 10. I am calculating it over here. Percentage profit is 10. Profit in rupees is 63. Cost price do we know? No, we don't know. Into 100. So, what do we get the cost price as? Rupees 630. This is the cost price of the book. Now, we know that profit of Raj was rupees 63. That means the selling price for Raj. must have been the cost price plus the profit that is 63 rupees that is rupees 693. So this is the price at which Raj sold the book to Simran but we already know that Raj should sell the book to Simran at rupees 77 m by 100. So that means these two values have to be equal. So let us write them down 693 equal to 77 m upon 100 let us see this is divisible by 7 this is divisible 7 9s are 63 so 9 comes over here again 63 99 11 into 9 so marked price becomes rupees 900 so this is the marked price of the book which raj sold to simran see how easy discounts was if you know percentage you would very easily solve all the sums related to discount whenever you have discount you either find the discount discount in rupees. Okay, if you have discount in percent find the discount in rupees or find the price of the object after cutting the discount, right? And after that there are also things which we saw like profit and loss and this formula related to profit and loss which you which is useful later on to now we have seen also remember list price is greater than selling price is greater than the cost price. We also saw formula for successive discounts what was it at the center. here I'm writing add minus multiply divided by 100 to get the successive discounts. This ends the video on discounts. Give it a like if you liked it and please share it with others. Comments and suggestions can be left in the comments box below. Do let us know if you have a topic in mind and we will develop a video on it for you. Don't forget to subscribe to our channel and stay updated for more such tutorials.

Today, we will learn how to pick solve all types of discount sums that may be asked in exam. You can practice discounts and other quantitative aptitude topics on careerright.com which has 1000 plus aptitude questions and practice test for you. So let's get started.

Let's get started. Let us understand what is the meaning of discount. Now say this is a book and the price of the book is say rupees 250. If you are buying this book and say if the shopkeeper is giving you say 50 rupees off or 50 rupees discount. So what does that mean?

That means you have to pay 50 rupees less. That means the price of the book now for you would be 250 minus. 50 equal to rupees 200 that so discount means paying less amount of money or giving less that is the meaning of discount generally discount is can be given or expressed in terms of absolute values like 50 100 etc or it most of the times like say in most of the sums discount is expressed in terms of percentage that is 10 percent 12 percent okay whenever you go out for shopping you will see that there is flat 50% off then there's up to 40% off and all this stuff so this off which is given flat 50% off or 40% off that is nothing but discount right so discount is nothing but paying less money so now if say if this is a book and if a person is giving 10% discount on this that means you have to pay 10% less amount of money so how much money you will actually pay that would be total percentage we have seen That is nothing but anything, any object which is there that is always taken as 100%.

That entire object is 100%. Now price of the book is 250. So 250 price is nothing but 100%. Out of that discount is 10%.

So minus 10%. So you will get 90%. So the price of the book now is 90%. So you will just have to pay 90% of 250 rupees.

And that is nothing. but the price of the book for you. So whenever they have given discount it means that you just have to remove that percentage from the from 100% and that remaining thing is nothing but the price that you have to pay.

Now there are some terms which are very important and are related to discount. Let us see what the terms are. The first term is marked price. See on the left hand side corner marked price.

Second is list. price. Third is advertised price.

Okay. Advertised price. All these three things mean the same.

Now let us see what these three things mean. Let us say on the over here we have our book. Okay. Price of the book is 250 rupees. That is nothing but the marked price or list price or advertised price.

This is the price which is written on the book. That is 250 rupees. On that the shopkeeper gives say 10 percent. discount okay so this is nothing but discount so how much now the book will cost now 10 of 250 what is 10 of 250 just put a decimal point so 10 is nothing but 25 rupees so 25 rupees is discount so now the price is 250 minus 25 that is 225 rupees this is nothing but the selling price of the book so shopkeeper will sell the book after discount will sell the book at this price 225. So what do what have we seen over here see at the right hand side bottom marked price is always greater than selling price.

So marked price or list price or advertised price is always greater than selling price because we give a discount on marked price and then we subtract the discount and whatever is the remaining at that price we sell the book. So that is the selling price. So marked price is greater than selling price. So remember Remember this.

Okay. Now, let's move on to another concept called as successive discounts. Many a times in exam you will come across a problem which says that a person got too successive discounts okay two successive discounts of say 10 percent and 5 percent.

So what is the equivalent discount? Now what does successive discount means? For example if an object is of say 1000 rupees then the first discount would be 10 percent right then we will reduce this 10 percent from this 1000 rupees then we will get some price say it is A B C then again we we will give a discount of 5% on this price, this new price and then we get the final price.

So, this is nothing but successive discounts. First discount, then the second discount. Now, instead of calculating it by this method, there is a very very simple and small formula or a tip we can call it. Tip we can call it to find equivalent discount. For example, if there are two discounts of 10%.

and 5%. Then what is equivalent single discount? That means on combining these two, what exactly amount, what percent discount the person finally gets. So, single equivalent discount can be given by add minus multiply.

by 100 whenever there are two discounts single equivalent discount of these two discounts is given by add minus multiply by 100 what is add add is nothing but add both the discounts 10 percent 5% minus multiply multiply means multiply both the discounts 10 into 5 upon 100 what we get over here 15 minus this is 50 upon 100 that is 1 by 2 that is 0.5 15 minus 0.5 is 14.5% so this is nothing but successive discounts this is the formula to find single equivalent discount instead of single equivalent discount of two separate discounts two successive discounts if there are three successive discounts we will find it out later on how to tackle that but if there are two successive discounts we can find the single equivalent discount in relation to these two successive discounts by this formula. What is the formula? Add minus multiply by 100. Add minus multiply by 100. Remember this 100 is under multiply. It is not under add.

Okay. It is add minus multiply by 100. Add minus multiply by 100. Let's see some of the sums related to discounts. Question number one. During monsoon clearance sale, Amit buys a shirt at double discount of 20% and 10%.

Okay. At what price he bought the shirt if marked price was Rs.1000 that means there was a shirt over here there was a shirt and there was a price tag that means marked price was Rs.1000. Amit got a double discount 20% and 10% that means he got successive discounts. And we want to find out at what price he bought the shirt.

Now we can solve it in two ways. One is by the successive discount tip which we learnt earlier and one is by normal way. So in this way we can solve the problem.

instead of solving by successive discount way, we will do it by the normal way because ahead we are going to use the successive discount tip. So let's now solve it by normal method. So price of the shirt is 1000 rupees.

How much was the first discount? 20%. So what will be the price of the shirt now? 100% minus 20%.

That would be 80% of the discount. marked price. Why? Because 20% discount has been subtracted out of the total price.

20% discount is subtracted. So what remains is just the 80%. So Amit has to pay now 80%. What is this 80% of marked price?

Percentage means we know divide by 100 of his multiplication mark price is 1000. This is 10. So 800. So after giving 20% discount, the price of the shirt becomes. 800 rupees now take this 800 over here this is the new price right now again amit gets 10 percent discount on this 800 rupees right so what is the price now it would be 100 percent Minus 10% that is nothing but 90% of this new price that is 800 rupees. That would be 90 upon 100 into 800. This gets out so 720 rupees.

So the final price at which Amit bought the shirt was 720 rupees. See how easy it was if we know the percentage discount. If you know the percentage discount, what we can do is we can simply subtract it and get directly the price of the shirt after discount. Or there is another way what you can do is 20% discount is there.

So what is 20% of 1000 that is nothing but 20 upon 100 into 1000 that would be 200 rupees. That means discount is 200 rupees. So the new price is 1000 minus 200. 800 rupees same way now the price is 800 discount is 10 percent 10 percent of 800 is 80 right so now the new price or the final price which amit pays is 800 minus 80 rupees that would be rupees 720 both ways it is same okay this way or this way both it is same we get the same answer moving to question number two if successive discounts are 15 percent and 10 percent Then what is its single equivalent discount?

Now what tip we have seen single equivalent discount of two successive discounts is nothing but add minus multiply divided by 100. So what it would be 15 plus 10 minus 15 into 10 divided by 100 that is 25 minus 10 10s are 1.5 that would be 23.5 percent right this is the single equivalent discount let us prove this that this is the single equivalent discount let's see how Let us assume the price is 100 rupees of an object. First discount is 15%. 15% discount is first. So what is the price now? That would be 100% minus 15%.

That would be 85% of the original price. Original price. That is 85% of 100. That is rupees 85. So new price is 85. Now 85. rupees is the new price second discount given is 10 percent okay what is the final price 100 percent minus the 10 percent discount so the person has to pay 90 percent of the new price what is the new price 85 rupees so person has to pay 90 percent percentages divided by 100 of 85 rupees that is 90 into now this is nothing but 0.85 85 divided by 100 take this 10 take this 0 over here you will have 9 into 8.5 that would be 9 5s are 45 decimal 9 at 72 and for 76.5 so the person has to pay 76 rupees and 50 pesa right original price was 100 rupees the person is paying 76.5 rupees difference is rupees two 23.5 now 23.5 is nothing but the discount which the person has got right now 23.5 rupees is nothing but discount on the original price of rupees 100 so what is 23.5 how much percent is 23.5 of 100 very easy quantity 1 upon quantity 2 23.5 how much percent is 23.5 of 100 and since we want percent multiply by 100 what do we get 20. which is nothing but this which we calculated. So see here we showed instead of calculating such in a such a big manner, okay, such a big manner much better use this formula for finding successive discounts. It is very easy to remember you don't have to do anything just remember add minus multiply by 100 add minus multiply by 100 even if you repeat it 10 times you will be able to remember it immediately over here.

Moving to question number 3. Question number three if successive discounts are 10% 20% and 30% Then what is its single equivalent discount now earlier? We saw two successive discounts now here We have three successive discounts what to do Do not worry again. This is very very easy to solve.

Let us see how to do it. 10% 20% and 30% Okay, these are the three discounts first take. any two let us say i take 10 and 20 find the equivalent discount what is it equivalent discount is add minus multiply upon 100 what do we get 10 plus 20 minus 10 into 20 upon 100 what do we get over here 30 minus this is 200 upon 102 we get 28 percent right this is we write it over here year 28 percent equivalent discount of these two is 28 percent now take this take the third discount and find the equivalent what it would be add minus multiply divide by 100 so that would be nothing but 58 minus the zeros get cancelled we have 2.8 into 3 that would be 58 minus 8.4 that would be 49.6% this is the single equivalent discount in relation to the three successive discounts that we you that you get if there are four discounts say one two three and four what will you do find equivalent of this find equivalent of this and whatever the answer you get here and here find equivalent of this and you get the answer final answer or single equivalent discount see it is very easy just remember this small formula and you will be able to solve the sums moving Moving to question number 4. Two successive discounts with the first being 20% were given on a table having marked price of Rs. 6400. Finally, it was sold for Rs. 4608. How much was the second discount?

Again, very easy. This can be solved in two ways. One by the successive discount formula and one by normal way.

Let's solve it by the normal way instead of successive discount method. That is also easy. But let's go on with the normal way.

Now the first discount is 20%. Do we know the second discount? No. Let us assume the second discount to be A%. What have they given?

Marked price is 6400 rupees. 6400. The first discount given is 20%. Right. So what will be the price after discount? It would be 100% minus 20% discount.

That would be 80% of the marked price or the original price. That would be 80%. upon 100 into 6400 okay what do we get over here 614 to 8 I shifted the 0 over here because it makes easier it makes the calculations easier we get 8 0 0 8 4s are 32 8 6 of 48 50 and 5 1 2 0 now this is the price after the first discount take that price over here now the price is 5 1 2 0 now the second discount that is given one is a percentage right so now what is the price that the person has to pay after a percent discount that would be 100 percent minus a percent right this is the price the person has to pay that is nothing but 100 minus a percent right 100 minus a percent is the price that the person has to pay after a percent discount and 100 minus a percent of the new price what is the new price 5 1 2 0 ok So what that would mean 100 minus A upon 100 because percentage sign is divided by 100 multiplied by 5120. This is the price which the person has to pay or the table is sold at after giving the second discount.

Now but they have given that the table was sold for 4620. 46 sorry 08. 4608 rupees after giving two successive discounts. That means 4608 rupees is nothing but this price. Right.

Right whatever we have found out it is nothing but this price over here. So let's calculate what do we get over here 100 minus a upon 100 would be equal to 5120. Okay, that would be 4608 divided by 5120. Now this looks like it is divisible by 2. So 2 2's are 4 4 1 2 2's are 4 11 2 5's are 10 6 2 5 6 0. So here we have 2. 3 0 4 okay now again this looks like it is divisible by 4 let us see what do we get 4 6 are 24 16 640 this is divisible by 4 4 5s are 37 26 5 76 6 this is divisible by 8 80 okay 8 into 80 8 7s are 16 2 so we get 72 upon 80 okay 8 10s are 8 9s are. So what do we have? Let's calculate it over here on the right hand side. We will have 100 minus a upon 100 would be equal to 9 upon 10 okay this goes over here 100 minus a okay this 100 minus a would be equal to 9 so a would be equal to uh 90 9 and 10 90 a would be equal to 10 percent so the second discount is nothing but 10 percent see how easily we got it in exam with practice you will be able to solve this sum in hardly say 30 to 40 seconds okay this is very very easy you just have to calculate It took time to calculate over here, but I calculated it to show you that these can get divided you will get better answers.

You can be very quick at calculations and you will get the answer very very quickly. Now moving on to question number five. Sonali could not decide between discount of 30% or two successive discounts of 25% and 5% both given on shopping of rupees 2000. What is the difference between both the discounts now over here we will solve this by the successive discount tip which we have seen earlier what is it it is nothing but add minus multiple multiply divided by 100 right add minus multiply divided by 100 what have they given over here Sonali does a shopping of rupees 2000 she is given two choices she can either get 30% discount okay or she can have two successive discounts of say 25% and 5% right now she cannot decide between the two discounts what we have to find is the difference between both discounts right so let us see what to do now shopping is of 2000 first option is of 30 discount so how much is she saving or how much discount in rupees is she getting that is nothing but 30 percent of 2000 that would be 30 upon 100 into 2000 that would be 30 into 20 that would be rupees six 600. So in the first case Sonali is saving rupees 600. Sonali is getting a discount of rupees 600. Now let's see in second case we have two successive discounts. So what would be the single equivalent discount for both of them? Add 25 plus 5 by multiply 25 into 5 by 100. This is 4 5 by 4. So we will have 25 30 minus 5 by 4 that is 1.25 that is 28.75.

percent right so she gets 28.75 percent discount in the second case so how much in rupees is she actually saving or getting the discount that is nothing but 28.75 percent of 2000 right that is nothing but 28.75 upon 100 into 2000 this gets cancelled we will get 28.75 75 into 20 so multiply by 2 what do we get 2 5s are 10 2 7 14 15 2 9 2 8s are 16 17 2 to the 4 5 multiplied by 10 that would be 575 rupees so in second case she gets discount of 575 rupees in the first case she gets discount of 600 rupees so what is the difference between both discounts 600 minus 575 that would be rupees 25. So the difference between both discounts is rupees 25. Moving on. Question number 6, which of the following will yield maximum discount on Rs. 6896? First is two successive discounts of 5% and 5%, second is single discount of 10%, third is two successive discounts of 8% and 2%.

Now, you might think that this is pretty lengthy also the number given over here is looking a bit difficult and calculation will take time but no this is very very easy. Okay, let us see how to solve it. You know the formula for successive discount.

that is nothing but add minus multiply by 100. Okay, and you just need to find out which of the following options will give you maximum discount. Now, say if you get a discount of 10% on one object and say 20% on the same object, then which of this option will give you maximum discount, but obvious this 20 is more than 10. So 20% discount means you'll get more discount than this same way over here, we need not consider the at all do not consider over here the amount just find single equivalent percentages of these and whichever percentage is higher that will give you maximum discount see how easy it was let's see the first option what is the first option two successive discounts of 5% and 5% so what is the single equivalent of this add minus multiply divided by 100 that would be 10 minus 2 or 25 upon 100 is 1 by 4 that is 0.25 that is 9.75 percent second one is very easy it is given single discount of 10 percent so it is 10 percent only third one two successive discounts of 8 percent and 2 percent what is the equivalent of this 8 plus 2 minus 8 into 2 by 100 10 minus 16 upon 100 okay now instead of calculating this we just want the max maximum discount no need to go into its calculation why 10 minus that means something is going to get subtracted from 10 is that right that means the value will be less than 10 we already have 10% over here right so this is nothing but largest okay amongst 9.75 10% and some value which is little bit less than 10 largest is nothing but 10 so this is the one this option will give you maximum discount See how easy it was in exam you will be able to solve this in hardly 15 seconds. 15, 10 to 15 seconds or sometimes always remember a small trick.

Say if the percentage now over here is 10. 10%, single discount of 10%. Now these two successive discounts are 5% and 5%. If you add 5 plus 5 what you will get?

You will get 10. If you add this 8 plus 2 what you will get? You will get 10. Whenever such options are there, always remember the single equivalent discount of 10% will always be there. always be greater than two successive discounts whose addition is 10. For example, let us say a discount is given of say 15%, single discount of 15%.

This will always be greater than successive discount of 10% and 5% or say take any value 2% and 13% addition of these 10 and 5 is 15, 2 and 3 is 2 and 13 is 15. So, greater than this is nothing but single equivalent discount of 15%. You saw over here. 2 successive discounts equivalent discount came out to be 9.75 which is less than 10. Always remember single equivalent single discount not equivalent discount single discount is always greater than successive discounts of the same value.

Now moving to question number 7. Raj decides to sell his watch at 5% discount. But his brother buys it from him and he gives his brother 8% discount. Due to this, Raj gets Rs. 45 less in profit. the marked price of the watch.

Now, over here, what happens is that Raj wants to sell a watch. So let us assume that this is the watch. And the marked price for the watch is say, M rupees. Now Raj decides to sell the watch at 5% discount.

But his brother is buying the watch. Because of which what happens to the brother? He gives 8% discount.

That is 3% more. Plus 3%. 3%.

Because of this what happens? Raj gets rupees 45 less in profit. What does that mean? The 3% discount which Raj gave on the marked price. 3% more discount which Raj gave on the marked price gives.

him 45 rupees less that means this 3% on the mark price is nothing but 45 rupees had he given 5% discount only he would have got the same price as the previous one which he had decided but because of this 3% extra discount he gets 45 rupees less that means this 3% discount is 45 rupees that is 3% discount on mark price is rupees 45 so what we have to find is the mark price very easy 3 upon 100 because percentage sign is 100 multiplied by Marked price 45, 15. Marked price is Rs.1500. See how easy it was. Going to next question.

Ramesh was getting two offers on a book having marked price Rs.800. Either two successive discounts of 20% each or two successive discounts of 30% and 10%. If Ramesh chose the better scheme how much more he must have saved compared to the other scheme again very very easy we know the formula for successive discounts add minus multiply by 100 okay what is the first option given to successive discounts of 20 percentage so equivalent discount would be 20 to plus 20 minus 20 into 20 by 100 that would be 5 this would be 4 so this would be 40 minus 4 equal to 36 percent what is the second option given 32 successive discounts of 30 and 10 so add minus 30 into 10 upon 100 that goes out to 40 minus 37 percent that means ramesh gets one percent more discount in the second case here it is 36 percent here it is 37 percent so ramesh chooses this scheme better scheme now they have asked how much more he must have saved compared to that other scheme that means when he chose the second scheme how much more did he save he saved one percent more why because 37 minus 36 percent is one percent so he saved one percent more now one percent which is there that has to be calculated in terms of rupees so that one percent saving is nothing but one percent of 800 rupees that would be equal to 1 upon 100 into 800 equal to rupees 8 so Ramesh says rupees 8 more while choosing the better scheme see how easy it was using the simple formula there was 25% off on handbags Madhu bought a handbag she also got a 10% discount for paying cash she paid rupees 405 what was the price tag on the handbag again very easy some let's see to solve it there were there was handbag there was 25% off on it okay we do not know the price of the handbag so let us assume the marked price be M rupees on that Madhu got 25% discount okay after deducting 25% she there was some price on that again she got 10% discount right and then she paid the final bill after these two discounts final bill was rupees 405 they have given 405 as the amount which she paid now what does this mean she got two successive discounts of 25% and 10% so what is the single equivalent discount of these two we know the formula for single equivalent discount add my add minus multiply upon 100 so what do we get we get 25 plus 10 minus 25 into 10 divided by 100 so that would be 35 minus 2.5 that would be 32.5% discount so madhu in total got 32.5 percent discount so what price did madhu pay she simply paid 100 percent minus the discount okay that is 67.5 percent amount so she paid 67.5 percent of what of the marked price right so she paid 67.5 percent of marked price but we already know that madhu paid 405 as the final bill so 67.5% of mark price is nothing but Rs. 405. So what would be the answer?

Let's solve it. 67.5 upon 100 because percentage sign is divided by 100. Multiplied by M equal to 405. Let's divide by 5. We have 81 over here. We have 5 1's are.

5 3's are 15. 25 13.5 over here. Let's see if this is divisible by 3. Yes. 3 2's are 6. Then we'll have 21. 27 we get over here 3 4s are 12.5 4.5 okay again so we will have over here 4.5 into m is equal to 2700 right so again let's see whether this is divisible by 5 we get 0.9 over here we get 5 5s are 25 24 0 yes that would be m equal to 540 upon point point nine that is nine point ones are nine 60s are that would be 600 rupees 600 so the marked price is rupees 600 see how easy it was to calculate the answer moving to the next question question number 10 chandrika raised the price of their products by 40 percent how much discount should they give so as to sell the products on no profit no loss basis. Now, this looks a little bit tricky or complicated not much is given over here.

But to solve such kind of sums, okay, let us use a very, very small tip or a trick that would make this very easy. Now in percentages, okay, this will make it very easy, right. So now in percentages, what we have seen is that whenever we do not know how to proceed, what we do, let us assume that the price of the product is rupees 100. Right?

Now this will make it easier. Now they raise the price. price by 40% so price is increased by 40% more that means 40% of the original price that is 100 so rupees 40 more so price is increased by rupees 40 more so what is the new price new price is rupees 140 now new price is rupees 140 so do not consider the old price at all right now what are they what are they saying is that how How much discount should they give so as to sell the products on no profit no loss basis?

Original price was 100 rupees. New price is 140 rupees. That means it is 40 rupees more.

So if they want no profit no loss then they should reduce the price by 40 rupees. Is that right? Did you get it?

If you reduce the price by 40 rupees and sell the product at 100 rupees you will be on no profit no loss basis. Right? So what to do now?

So we know that Chandrika. should give a discount of rupees 40 right but we want this discount in the format of percentage so how to calculate how much is 40 percent of 140 why did we take 140 and why did we not take 100 because the new price is 140 now we should not consider 100 anywhere so how much is the discount 40 rupees of 140 we have learned in percentage quantity 1 divided by quantity 2 multiplied by 100 because we want percentage. So what do we get over here? 400 divided by 14 that would be 200 divided by 7 that would be 7 twos are 14 67 eights are 56 47.5% so approximately 28.5% discount has to be provided by Chandrika so that they give rupees 40 off and so that they'll sell the products on no. profit no loss basis see how easy it was I'll explain again 40% increase in price so the price becomes 140 if they want no profit no loss they have to reduce 40 rupees give the discount of 40 rupees so that original price again becomes 100 rupees but what is 40 rupees discount in terms of percentage 40 upon 140 into 100 why 140 because new price is 140 we should not consider old price now that gives out 28.5% discount. Thank you.

Question number 11. There is a 10% discount on a dozen pairs of trousers marked at Rs. 8000. How many pairs of trousers can be bought with Rs. 2400? Very easy. Dozen pair of trousers means 12. 12 pairs of trousers. Cost of 12 pair of trousers is 8000 rupees.

This is the marked price. Now there is a 10% discount if you buy 12 pair of trousers. 8000 rupees that would be 10 percent of 8000 rupees that is nothing but 800 rupees right 800 rupees is the discount so the final price now is rupees 7200 that is 8000 minus 800 right this is the final price now 12 pairs are bought for rupees 7200 so one pair of trouser is bought for 7200 divided by 12 that is rupees 600 Right? Now we have 2400 rupees with us. In 2400 rupees how many pair of trousers can be bought?

One can be bought in 600. So in 2400, 2400 divided by 600 that would be 4 pair of trousers can be bought in rupees 2400. 4 pairs of trousers. This is the answer. Question number 12. Blackberry announced a discount of 25% on their trousers. Vivek went to shop.

He He wanted to save rupees 400 in discount. How many trousers should he buy to do so? If each trouser costs rupees 320, cost of each trouser is 320, discount on each trouser is 25%.

So how much is the discount in rupees? That is nothing but 25% of 320. That is 25 upon 100 into 320. 25 fours are rupees 80. So each trouser Vivek can save rupees. rupees 80. Now he wants to save 400 rupees in discount.

Here in each trouser he is saving 80 rupees in discount. So how many trousers he should buy so that he will save 400 rupees in discount. Total rupees in discount he wants to save divided by amount of rupees he saves in one trouser. That would be 5 trousers.

So if he buys 5 trousers he will save 80 rupees for first, second, third, fourth and fifth and this total is 100 rupees. So he will save total will give him Rs. 400 savings in discount. So he needs to buy 5 trousers.

Question number 30. How much does the sarees sales revenue of Uday increase if Uday announces 25% discount on sarees and the saree sales volume increase by 40%? Again over here we do not know exactly how much is the revenue earlier, how much is the revenue later and all that stuff. So let us start by some assumption. Let us say that Uday sells say 10 sarees and price of each saree is rupees 100. So what is the revenue of Uday? Revenue of Uday is nothing but 100 rupees each saree into 10 sarees that is rupees 1000. This is the initial revenue of Uday.

Now what does Uday do? Now Uday gives a 25% discount on sarees. So now initially the price was 100. 25% discount.

Okay. So what will the price? 100% minus 25%.

That would be 75% of 100. Right. That is nothing but rupees 75. This is the new price of saree. Right. Also they have given that the sales volume of saree increases by 40%. Initially Uday was selling 10 sarees.

Okay. Now there is a 40% increase in the sale of sarees. In the number of sarees which are sold. So what is 40%?

percent of 10 it is nothing but 4 correct so 4 is the 40 percent of 10 that means Uday is selling 10 plus 4 equal to 14 sarees now right this is the new volume right this is the new volume now what is the new revenue of Uday 75 rupees each saree into total number of sarees sold is 14 that is 1050 rupees this is the new revenue of Uday. So, what we have to find out is how much does the sarees sales revenue of Uday increase. So, new revenue is 1050, old revenue is 1000. So, the increase is rupees 50. 1050 minus 1000 that is increase is rupees 50. That is the rupees 50 increase. Now, if we have to calculate it into percentage, what we will see? We will take 50. How much percent increase is there if we have to find out?

what we will do Take 50 divided by the new old revenue because we have to find out how much increase is there as compared to the old revenue right. So 50 upon 1000 into 100 since we want percentage. This gets cancelled this gets cancelled that is 5 percent increase in revenue.

Moving on to question number 14. Question number 14. If a book costs Rs. 900 and is sold with a profit of 10% and discount of 12%, then the advertised price is... Now, this is a very easy sum. This might look complicated to you, but it is not.

You just need some common logic over here that would be helpful to solve the sum. Let us see. There is a book.

Now, there is some advertised price or marked price or list price to it. Let us say we do not know that price. We have to find it.

Let us say M rupees is the advertised price of it, marked price of it. Now the book is sold at discount of 12%. So what is the price of the book at which it is sold?

It will be 100% minus the discount of 12%. That would be 88% of the original price or 88% of the advertised price or the marked price. That is 88 M upon 100. So the book is sold for... 88M upon 100 rupees.

Okay. Now, what have they given? The book costs rupees 900. So, the cost price of the book, that is the book at which the book is made is rupees 900. And it is sold with a profit of 10%. Now, let us say, let us take a very small example.

Say, if you have an object. Okay. Price of it is rupees 100. And you want to sell it with a 10% profit.

What you will do? You will take 10% of 100. 100 that would be rupees 10 and you will sell the book for your cost price plus this 10 rupees profit that is 110 rupees right so cost price is 100 and if you want 10 percent profit you sell it for 110 rupees let us see how 110 rupees converts to 10 percent profit 110 rupees is the selling price it is rupees 10 great rupees 10 greater than the cost price so the profit is rupees 10 is 10 and the cost price is 100 into 100 right that is nothing but the 10% profit right we know quantity how much more is the selling price than the cost price quantity 1 divided by quantity 2 and since we want it in percentage we multiply by 100 so 10% more so over here also cost price cost price is 900 rupees we want 10% profit right so what is 10% of 900 that is simply rupees 90. So the shopkeeper or the person who is selling the book, he has to sell the book at 900 plus 90 equal to rupees 990. Then only the person will get 10% profit while selling the book. Did you understand? It's very easy.

Cost price is 900 and the person wants 10% profit while selling the book. So he has to sell the book at 900 rupees plus the 10% profit. That is nothing but 10% of 900 that is 90 rupees and hence the person has to sell the book for 990 rupees but we already know okay this is the price for which the books need to be sold okay book needs to be sold now we already know that the book should be sold at 88 M upon hundred and we also know that the book should be sold for rupees 990 that means these two values are equal so equating them what do we get 88 M you upon 100, 118 Zaar, 119 Zaar, 90 Zaar.

So what do we get over here? We have 9000 divided by 8. That would be 8 1 Zaar. Again 8 1 Zaar, 8 28 2 Zaar, 48 5 Zaar. So rupees 1125 is the marked price of the book.

next question. Question number 15. Profit of Raj while selling a book to Simran is Rs. 63. Despite a discount of 23% on the book, Raj manages to get 10% profit. What must be the list price of the book?

Now this sum is very easy actually but you need to know one very small concept. It is very easy. It is related to profit and loss.

This formula which I will be telling you right now. you will have to learn it when it comes to profit and loss because otherwise you won't be able to solve the sums right so the profit and loss formula which i am going to you it is like this percentage profit is nothing but profit in rupees okay profit in rupees divided by cost price multiplied by 100 so percentage profit is nothing but profit in rupees divided by cost price multiplied by 100 you have to learn this formula we'll see in detail about this formula in the profit and loss video but over here we need this concept because many sums related to discount are connected to profit and loss also. So let us see how using this formula will arrive at our answer.

Now there is a book. Okay, there is a book and we do not which is sold by Raj to Simran now we do not know the list price of the book list by price means advertised price or marked price right marked price let us assume that the marked price of the list price is rupees M what have we learnt list price or the marked price is always greater than selling price and if you want to get a profit we know it is common sense selling price has to be greater than the cost price then only we will get profit otherwise we will have loss right just remember this it would be useful again when you you do profit and loss. Okay, now let the marked price be m rupees. Now Raj gives a discount of 23%.

So how much would be the selling price of the book that would be 100%. That is the price of book minus 23% discount, that would be 77% of the original price, that means the marked price. So the book has to be sold at 77% of m that is rupees 77 divided by 100 multiplied.

by M. So the book has to be sold at this price by Raj because he is giving 23% discount on the book. Now what have they given profit of Raj? Raj manages to get 10% profit right.

This is 10% profit but they also say that profit of Raj while selling a book to Simran is Rs. 63. That means this 10% profit is nothing but Rs. 63 right. This 10% profit in rupees is nothing but Rs. 63. So, using this formula now, let us see what do we get? Percentage profit is 10. I am calculating it over here.

Percentage profit is 10. Profit in rupees is 63. Cost price do we know? No, we don't know. Into 100. So, what do we get the cost price as?

Rupees 630. This is the cost price of the book. Now, we know that profit of Raj was rupees 63. That means the selling price for Raj. must have been the cost price plus the profit that is 63 rupees that is rupees 693. So this is the price at which Raj sold the book to Simran but we already know that Raj should sell the book to Simran at rupees 77 m by 100. So that means these two values have to be equal. So let us write them down 693 equal to 77 m upon 100 let us see this is divisible by 7 this is divisible 7 9s are 63 so 9 comes over here again 63 99 11 into 9 so marked price becomes rupees 900 so this is the marked price of the book which raj sold to simran see how easy discounts was if you know percentage you would very easily solve all the sums related to discount whenever you have discount you either find the discount discount in rupees. Okay, if you have discount in percent find the discount in rupees or find the price of the object after cutting the discount, right?

And after that there are also things which we saw like profit and loss and this formula related to profit and loss which you which is useful later on to now we have seen also remember list price is greater than selling price is greater than the cost price. We also saw formula for successive discounts what was it at the center. here I'm writing add minus multiply divided by 100 to get the successive discounts.

This ends the video on discounts. Give it a like if you liked it and please share it with others. Comments and suggestions can be left in the comments box below. Do let us know if you have a topic in mind and we will develop a video on it for you. Don't forget to subscribe to our channel and stay updated for more such tutorials.

Transcript for:Understanding Discounts and Calculations

Transcript for:
Understanding Discounts and Calculations