hello great 10 students today I am here with chapter 14 in your textbook that's called percentages first we will see why we need to learn about percentages for example I can tell you a story once two girls had a fight about their marks so the two girls were Sita and Mita Sita told that she got five correct answers out of eight questions Rita told that she got three correct answers out of five questions so Sita is telling she's the best because she got five correct answers but Nita is telling she's the best because she got two wrong answers that is less than what Sita got now we'll try to solve this problem so when we take as fractions for correct answers what can you say about Sita Sita got five correct answers out of eight what about Nita Nita got three correct answers out of five now now we need to compare these two fractions so how can we compare 5 over 8 and 3 over high if we can convert to the same denominator we can compare so here what's the common denominator lowest common multiple is 40 so I can take this one has 40 that means multiply by 5 5 times 5 25 here out of 40 what's the value of 5 times 8 8 times 3 24 now same denominator you can compare the numerator so which one is the best if we take this person so that's Sita so we can see Sita is the best one when we compare the correct answers now we see we'll take another person mala now mala also did the same test but she did 17 questions and out of 17 questions she got 11 correct answers now what happens now now 17 out of 11 out of 17 are correct now how can we find out which person is the best what happens now now again 40 and 17 different denominators we need to convert to the same lowest common multiple then it will get complicated and complicated because you have to take when the number of questions are different you have to take the lowest common multiple so it is easiest to take the 100 as the common denominator so what is a fraction with hundred as the denominator those are percentages so that's why percentages are important in maths so what we are we can do we can convert Sita's marks as a percentage value Mitas mark as a percentage value and Marla's also as a percentage value then you can find out easily who is the best so we are trying to find out here in percentages all converting all fractions decimal numbers to denominator hungry any value with the denominator hundred so what are percentages we can say percentages are fractions with denominator 100 okay we'll take a small number now if it's if we say 8 percent what is 8 percent means 8 over 100 I can write this one as 8 divided by 100 what can I do I can take this one and extend this line erase this number I can erase one and extend it then I get two zeroes I'll put one zero here is one zero and put put it here what happens I get this symbol this line with two zeros this is same as dividing by C dividing by 100 so this is called a percentage sign so we can write eight over hundred yes 8% so what's the meaning of percentage divided by 100 if this is 23 out of hundred I can write this one as 23 with this symbol it's divided by 123 percent so in this lesson we are using the symbol for percentage as this so remember the correct notation for percentages now we will look at these fractions and try to find out the percentage values 2 over 5 so what you do when you want to convert to a percentage you need to take the denominator hundred so I'm trying to multiply this by 100 in order to get cancel I'm dividing by 100 as well so what happens actually dividing by hundred means percentage sign so I can write this one as two over five times hundred as a percentage then you can simplify five times 20 20 times two this is equal to 40 per set now this is an improper fraction how can we find out the percentage value we can make it to this is a mixed number how can we convert to percentages first we can write as a improper fraction improper fraction 4 times 3 12 12 plus 3 15 over 4 now I can multiply and divide by hundred so divide by 100 ECMs the percentage sign so 4 times 25 25 times 15 25 times 15 what's the value 10 and 5 you get PI times 5 55 times 5 25 2 remaining 5 times 2 10 plus 2 12 so when you add it together you get 300 75 percent now look at these ones now we need to convert these decimals to percentages again what we do we'll multiply and divide by 100 I can't write like this basically 0.9 divided by 100 one two places to the right you get 90 percent this one multiplied by 100 and divided by hundred that means percentages now I'm not writing as divided by hundred I'm straightaway writing as percent th side so move the decimal place two places to the right you get 7 percent 2 point 8 multiplied by 100 you get one to two hundred eighty percent so how we convert fractions to percentages or decimals to percentages just multiply by hundred and make sure that you put the percentage sign convert these percentages to fractions now the reverse process of this so this is percentage sign means what we are dividing by hundred now you can simplify five times 111 and 5 times 20 so what the fraction 11 over 20 this one 3 1 eights you can convert to improper fraction so what's the answer eight times three twenty four twenty four one plus one twenty five twenty five over eight divided by hundred divided by hundred you can write as x one over hundred now simplify 25 times 125 times four you get 1 over 32 as the fracture now decimal value is there again percentage means divided by hundred five point eight divided by 100 now you can't keep decimals in fractions so we have to get rid of this decimal point multiplied by ten you get 58 you have to do the same thing for the denominator so you get thousand 58 Oh a thousand simplify 2 times 2 for 2 times 9 2 times 5 so what's the fraction 29 over 500 now we'll take these percentages to decimals 45 percent so what is 45 percent means 45 over hundred how can we divide by hundred move decimal place to two places to left 0.45 on two then 9.3 divided by hundred so again divided by hundred mean move this decimal place two places to the left one to 0.09 three one two then this one 223 percent 223 divided 501 to 2.23 is the decimal value now we'll take this number 24 percent to a fraction decimal and a ratio so how we convert to a fraction this one percentage sign means divided by 100 so 24 divided by 100 you can simplify further divide by 2 you get 12 divided by 2 you get 50 divided by 2 again 2 times 6 2 times 25 so 6 over 25 as a decimal you can write the same thing 2,400 and you can hear it abide by hundred how we divide by 100 moved the decimal place two places to the left so you get zero point 2 4 how can we write as a ratio so we can write ratio with the fraction so we found out the fraction as 6 over 25 same thing you can write as a ratio this is 6 to 25 we use the colon symbol for ratio fill in the blanks you have given the ratio and you're asked to write down the fraction decimal and percentage value so tow to 5 we can write as 2 over 5 as a decimal that means 2 divided by 5 long division for 20 that's 4 5 times 4 is 20 so zero point 4 is the decimal value so how can we find out the percentage value be multiplied by hundred four multiplied by hundred you get 40 so answer is forty percent three to four is the ratio you can write the fraction as three over four three over four long division 3 divided by 4 4 times 0 for 30 that's 7 28 for 20 that's 5 so 0.75 what's the percentage value this one the decimal value I can multiply by 100 move the decimal place two places to the right I get 75 percent is same as 3 over 4 or 3 to 4 ratio problems related to percentages so when we think about problems you get only three types of questions the first one is you will get a number and a percentage value so you are asked to find out the appropriate part so we'll see how we can solve a problem like this a percent of 400 so what we do 8 percent means 8 over 100 of means multiplication 400 is the valid now simplify hundred times 100 times 4 4 times 8 32 so this means if we take 400 values 8 percent is 32 so we can find a part of a percentage value now we'll take the same problem and do it other way around now the percentage is given and part calculated is given you are asked to find out the total amount so earlier question we found that 8 percent of this value is 32 now in this question I gave 8 percent is 32 you asked to find out the total value so how can we do this way if the 8 percent value is this one means 8 over hundred is 32 then what is one part one over hundred means you divide by 8 that's 4 one part is 4 so the full part made 100 paths so hundred over hundred it means four multiplied by hundred you get 400 so this is rupees so if you know one part and the percentage you can find out the total amount now we look at the third way of finding their answer in this question part value and the total amount is given you are asked to find out the percentage of that value that's the third time so when we are when we get the total parts so what we do as a fraction we can write 32 parts out of 400 is the fraction how we convert to a percentage you multiply by 100 percent so 100 into 400 is 4 32 divided by 4 you get 8 percent now we'll see we did three ways first the number is given and the percentage value is given we'll look at first part what's the first part given a number and the percentage so these two then you found out 32 that's what we did in the first part in the second question percentage and the part given so that is the second way of getting percentages and the third one we did and the third part what we did you have given the part and the number the part and the number given you can find out the percentage value so these are the three types of questions you can get in percentages now we look at review exercise in your textbook says complete the table by writing a suitable value in each empty box so first one already done for you you asked to find out this value percentage of this decimal how we do we can multiply by hundred so multiply by hundred means 0.6 multiply by 100 two places to the right you get sixty percent this one you are asked to convert to a fraction so 0.8 0.8 you can write as 8 over 10 now simplify 8 over 10 you get 4 over 5 this one easy to convert percentage to decimal 25 percent means 25 out of 100 you divide 25 by hundred move two places to the left the decimal place move two places to the left so 0.25 now the decimal form is given how do you find out the percentage multiply by 100 that means move the decimal place two places to the right get 6% now other way round you find out the fraction traction how can you fly find out 0.06 means six divided by hundred as a fraction six divided by hundred means to divide by 2 you get 3 divided by 253 over 50 and this one 8% is get given have you convert to a decimal eight divided by hundred means 0.08 now write as a fraction eight over hundred simplify further divide by two you get 50 divided by 2 again 2 over 25 question number two represent as a percentage 50 rupees as a percentage of 200 so how can we do that 50 rupees out of 200 you have to convert to a percentage so multiply by 100 100 times 250 divided by 2 you get 25% this one 20 cents as a percentage of one rupee here units are different so what is one rupee in cents hundred cents so you have to convert to the same units 25 cents out of hundred cents and when you want to convert to a percentage you multiply by hundred so one hundred and hundred get cancelled out you get 25% this one centimetres 8 centimetres with 2 meters again convert to the same unit meters you can convert to centimeters 100 centimeter is 1 meter so what is 202 meters means 200 centimeters in 200% 100 into 2 8 divided by 2 you get 4 percent 50 grams as a percentage of 1 kilo so what's the relationship between grams and kilograms thousand grams is equal to 1 kilogram so 50 grams out of thousand grams convert to a percentage by multiplying by it by 100 hundred and this zero get cancel out you get five percent 300 millimeter milliliters as a percentage of one lead so how many liters for one how many milliliters for one liter thousand three 300 divided by thousand multiplied by 100 two zeros get cancel out this one with this one you get 30% last one 15 students as a percentage of 40 so 15 out of 40 as a percentage you multiply by 100 zero zero get cancel out you get 2 times 5 - x - 15 x 575 divide by 2 you get 2 times 3 6 4 15 7 and 37 and a half or you can write as 37.5 as the decimal answer third one find the quantity 60% of 60% means 60 over hundred first off means multiply by five hundred 100 times five five time 60 you'll get 300 so this is an amount so 300 rupees this one 20 percent 20 over hundred in to two hundred fifty one zero get cancelled out this zero get canceled out 25 times 250 this is in kilo meters this one 25 percent 25 over 100 into 24 so 25 times 125 times 4 6 24 over 4 8 6 so what's the unit this is six of us this one three percent of two liters 3 over 100 I'll take two liters 2,000 milliliters then one zero get canceled out another zero so you get 3 times 2 60 milliliters is the answer fifth pot 15 percent 15 over hundred into one kilo one kilo I'll write as thousand grams to see rose 15 times 10 under and 50 grams this one 12% 1200 hundred into I'll convert meters to centimeters 1.5 is same as 150 centimeters now simplify 0 and divided by 2 divided by 5 divided by 5 is 2 divided by 5 3 then two and six you get six times three 18 centimeters you see answer now we'll look at what our taxes the government of each country collects money from its citizens to meet recurrent expenses so the government needs money so they are collecting money from citizens why they need money for recurrent expenses what are the current expenses to build high base and to pay salary of the government servers Oh when there's a natural disaster floods tsunami those disasters they need money natural disasters they need money natural disaster so that's those are recurrent expenses so this money is called taxes so government is collecting money from citizens we call those our taxes different types of taxes are collected in different ways and in barring amounts the method that is used most to collect taxes is charging a percentage of the amount involved so always charging a percentage taxes that an individual has to pay directly to the government are called direct taxes now these are direct taxes rates customs duty income tax but what are indirect taxes then indirect taxes are taxes that is not paid directly to the government indirect taxes have you heard about what value-added tax so what is that rekt means think about you're buying a loaf of bread from the shop so when you buy the loaf of bread you are paying a tax to the government how because the flour is imported by other country so we have to think about that value so they are charging a tax for importing flour so without knowing we are paying more than that so that's called that so that's indirect taxes we we are not paying directly but with the price of the object we are paying that amount so in this lesson we have to talk about all these types of taxes now we'll first take water rates grades are taxes charged by urban councils municipal councils and provincial councils so we are we need to give the money to a burn councils municipal councils and provincial councils from households and businesses that come within the administrative domain if you have a house or a land or a business we have to pay this tax these taxes are used for various purposes such that maintenance of roads and streetlights and garbage collection and disposal so what the government do they collect the money and again spending for garbage collection and disposal and road maintenance or streetlights so properties owned by individuals and businesses are assists annually by the government and the relevant council charge is a percentage of the assessed animal value of the property as rates this is calculated annually and can be paid in total at the beginning of the year or in four equal quarterly installments once every three months so every year you have to pay rate so assist a percentage value from the assessed value so you can pay at once or quarterly install months once in every three months do you know when you pay at once you get 10% discount so most of the people do they pay at once for the whole year because they are getting 10% discount now we'll look at example one a house of assessed annual value is thirty six thousand rupees is charged annual rates of four percent calculate the rates that have to be paid for a quarter quarter means four equal parts the assessed value divided by four is their quarterly value so we'll try to find out that value so what's the amount thirty six thousand rupees and four percent of that four percent means four hundred this is annual charge so two zeros get canceled out and then you get 4 times 0 0 4 times 6 24 2 remaining 4 times 3 12 12 plus 2 14,000 440 annually so what's the quarter leave valium quarterly value is you have to divide this by 4 4 times 3 12 for 24 48 so quarterly value is 300 80 rupees example to the assist annual value of the shop within the administrative domain of a certain urban council is 24 thousand rupees the quarterly rates payable on this property is 300 so quarterly value is given 300 calculate the rates percentage charged by the council now this is the quarterly value so what's the annual value they are paying annual value is you multiply by 4 300 multiplied by 4 that's rupees so you get 12 12 + 2 0 thousand 200 for the whole one year now what's the full amount is this so what's the percentage value so percentage value is equal to the amount you're paying for the whole year divided by the total amount and multiplied by hundred percent so simplify these two get cancelled out 12 times 1/12 times 2 and then once you get allowed 10/2 that's 5% now we look at what our customs duty when a certain items are imported or exported a certain percentage of the value of the item has to be paid as taxes to the government such taxes are called customs duty this tax is charged by Sri Lanka customs so we have to pay to the Sri Lanka Kuster why we are paying when you are importing or exporting any item they are charging a percentage for that individuals who have worked abroad are entitled to duty-free quota on their return which may be used to purchase certain items without paying customs duty from the duty-free shops so you know when you go abroad you can buy some of the items without the tax so we call those are items you can buy from duty-free shops and also certain government servants are entitled to a reduction in customs duty when importing vehicles so politicians doctors are some professionals are entitled for that so they can import vehicles without not without the renew reduction of the tax so we'll see how we can solve problems related to customs duty we'll take the example number one if customs duty of 10% of the value of the item has to be paid when a certain type of clock is imported how much duty has to be paid when a clock of this type value 5000 rupees is imported so what's the value five thousand so what's the tax percentage 10% of the valley so what's the 10% of the value multiplied by ten percent that means five thousand multiplied by ten over 100 zero zero get cancel out one so you don't get cancelled out so value you have to pay is five hundred rupees for the tax so they are asking how much do you T has to be paid when a clock of the time value five thousand is important so five hundred rupees they have to pay example number two when a car is important sixty percent of its value has to be paid as customs duty find the total amount with the duty included that it cost a person to import a car worth two million so what's the amount two million and what's the percentage of tax sixty percent sixty percent means sixty over 100 so what's the value you have to pay one zero get cancel out six times two twelve and how many zeros one two three four five so five zeros are there so what's the value how we read this 1.2 million and they are asking what's the total amount they have to pay this is the tax amount so the total amount you have to pay is the tax value 1.2 million plus two million of that so two million and 1.2 what's the total they have to pay so the total amount is three million two hundred thousand rupees now I'll do another method so straight away we can find out the amount you have to pay so what we do so if you buy four hundred rupees you have to pay sixty more so that becomes 100 and 100 plus sixteen hundred and sixty so if this is hundred you have to pay one hundred and sixty so if this is one you have to pay one hundred and sixty over hundred so we can take that value to find out the value straightaway so the initial by the amount is two million and then multiplied by one hundred and sixty over hundreds zero get cancelled out this zero get cancelled out with this zero 2 times 16 you get 32 how many zeros 1 2 3 4 5 2 3 4 5 then this becomes 3 million and 200,000 example number three if 18000 was charged as customs duty when a stock of fruits worth 300,000 was exported to the Middle East find the percentage of the value of the stock that the exporter had to pay as customs duty so what's the customs duty value 18000 what's the amount the total amount is 300 thousand so we can straightaway find out the percentage value is equal to 80 thousand for 300,000 and then convert to a percentage you multiply by hundred percent three three rows three zeros get cancel out these two zeros with this two and you get 18 divided by 3 6% custom duty has to be example number 4 the value of a television set with a 15% customs duty added to its value that's twenty eight thousand seven hundred and fifty what is the value of the television said without the duty so this one this value twenty eight thousand seven hundred fifty with this fifteen percent tax if you buy for 100 rupees then you have to pay 150 rupees if it's one part this is 115 over hardness now look at the value the value is with the tax so that means 115 parts represent twenty-eight thousand seven hundred fifty rupees so what's one hundred percent parts that that's the value without tax so you get twenty eight thousand seven hundred and fifty multiplied by hundred divided by 150 so divided by five 23/5 here 5 times 5 25 37 7 and again at the fire now multiply by 100 you get five seven five with three zeros divided by twenty three twenty three times two you get forty six remainder is universe 415 here for Olympia 415 how many 20 threes you get five five times three 15 one remaining five times two 10 10 plus 1 15 so you get 25,000 so what's the value without the tax 25,000 rupees now we look at what's income tax the government imposes a tax on the annual income of an individual which is earned as salary from property or through a business and which exceeds a certain limit such taxes are called income tax so here this is varying so this is the annual report in 2011 the income tax for a particular year can either be paid annually or in quarterly installments a table with information on how the taxes are calculated which was implemented in 2011 by the Inland Revenue Department is given below these values may change in the future but still they are using the same percentage here what it says so initially if this is the amount is you don't have to pay any tax but for the next 500,000 they are charging 4% for example if your salary is 1 million then you have to pay this 4% tax for only for 500,000 rupees then the next five hundred thousand eight percent so likewise can you see the percentage values these are multiples of four it's easy first five hundred thousand you don't have to pay any tax then the second five hundred thousand four percent the next eight percent four percent eight percent 12 percent like that so you need to know this table to calculate the income tax we'll take example number one the annual income of an individual is 575,000 calculate the income tax he has to pay for the year now first 500000 you don't have to pay so you subtract five hundred thousand from that so what's remaining you get 75,000 for 75,000 you have to pay four percent tax so we have to pay for percent tax for this value so what's the value seventy five thousand rupees multiplied by four over one hundred four percent value two zeros get canceled out four times zero zero four times five twenty two remaining four times seven twenty eight plus two thirty so so three thousand rupees for this amount so what's the total income tax value income tax value is 3,000 rupees example number two if the annual income of a certain businessman is 1 million six hundred fifty thousand rupees calculate the total annual income tax he has to pay so first five hundred thousand there's no tax so we have to subtract five hundred thousand from this yeah I'll write no tax for them for this amount we have to pay fire a 4% tax but now they're five hundred thousand so we have to take five hundred thousand four percent of that that means 20,000 for the first second 500,000 then I'll subtract that amount this is proficient then when you subtract 500,000 what's remaining you get 60 650,000 so from that you are you need to get 8 percent tax 8% for again 400,000 only for 500,000 you are charging for 500,000 so don't just multiply 64 650,000 by 8% only for 500 so what's the tax 8 times 0 0 8 times 0 3 0 is 8 times 5 14 so you will have to pay 40,000 for the next 500,000 now we need to subtract 500,000 from that so you get 150,000 so that's less than 500,000 so we need to pay for 8 then the 12% of that so 12 percent of that amount 150,000 12 percent of that 2 zeroes get cancelled out 12 times 0 0 0 12 times 566 remaining 12 times 1/12 12 plus 6 80 18,000 for this value so what's the total and we'll income tax value so you have to had all these text values so you get 0 0 0 8 4 + 1 5 5 + 2 7 so 78,000 you have to pay further and world tax now we'll look at value-added tax wet so that's indirect tax that we have to pay when a product or a service is bought a percentage of its value is charged as value-added tax the trader who sell the product and the service provider who are both bound to pay this tax charge it from the customer so when you go to a restaurant you are not only getting the amount for the food you have to pay a tax for that as well when you buy any item you are paying and for the services so when you go to a doctor so the hospital charge of tax from you so those are called wet value-added tax that's an indirect tax we look at example number 1 a certain person's monthly telephone charges are two thousand five hundred if a vat of 15% is added to this charge what is his monthly bill so 15 percent is added to this charge so 15 percent so first we can find out that value 15 percent of two thousand five hundred twenty-five times five is I'll do separately twenty-five times fifteen ten and five 375 rupees that's the tax amount so you have to pay extra for that so what's the total value of total value is the amount charged plus the batch value so you have to pay two thousand eight hundred seventy five rupees now we'll do the other method straightaway you can find so with the tax 15 percent text that means if you if the cost is hundred rupees you have to pay 115 so we'll take that to find out the tax so two thousand five hundred multiplied by one hundred and fifteen and divided by hundred so we'll do one hundred fifty three to be multiplied by 25 20 and 5 2 times 5 10 two times 1/2 plus 1/3 2 times 1 is 2 five times 5 25 - remaining 5 times 1 5 + 2 7 5 times 1 is 5 so you are getting the same answer 2875 example number 2 the production cost of a pair of shoes produced by a certain organization is given below the organization hopes to gain a profit of 250 from this product a wek of 15% has to be paid to the government on the price of the pair of shoes find the selling price of the pair of shoes with the vet included so what's the total cost thousand seven hundred now with the VAT so you need to first find the amount of VAT dog the price after adding the backed value so we'll find straight away the price after adding the bank value so what we do the cost is total cost is thousand seven hundred multiplied by this is percentage of where it is 15 percent that means 115 over 100 multiplied this 115 x 17 10 + 7 7 times 5 35 7 time is 1 7 + 3 10 7 times 1 7 + 1 8 so you get thousand nine hundred fifty-five with that that value now you need nother 250 profit so with that amount what's the price you need to consider to get this profit and this bat value you have to sell them sell this pair of shoes to this amount will calculate the value five ten twelve so two thousand two hundred hi so that's the amount you have to take exercise fourteen point one the assists annual value of a certain house is fifteen thousand if the relevant provision council institution charges five percent of the value of the house as rates calculate the rates that have to be paid for a year so what's the annual value annual value of certain houses fifteen thousand rupees so charging five percent as the rates calculate the rates that have to be paid so five percent of that value calculate the value here two zeros get cancelled out five times zero zero five times 5 25 two remaining you get 750 so the value is 750 question number two if the rates that have to be paid by a shop of assists annual value eighteen thousand is six percent of the value of the shop how much has to be paid as rates for a year so what's the value eighteen thousand and taking six percent from that so six percent of the value is the rates that you have to pay for the year two zeroes get cancelled out six times zero zero six times eight forty eight 6 times 1 6 plus 4 10 so I have to pay thousand 80 rupees for this yeah then they ask how much has to be paid as rates for a quarter quarter means every three months you have to divide the amount by four so two hundred seventy rupees you have to pay for a quarter question number three if two hundred seventy rupees has to be paid as quarterly rates for a house of assist annual value work eighteen thousand which lies within the limits of a certain urban council calculate the percentage that the urban council charges as rates so what's the quarterly value quarterly value is 270 then what's the annual Valley annual value is you multiply this by four thousand eighty rupees now the amount is eighteen thousand so what's the percentage of rates you are paying thousand eighty rupees for eighteen thousand convert to a percentage two zeros and this you get this one and divide by eighteen hundred and eight divided by 18 what's the value 6 so you get 6 as the answer so the answer is 6% question number 4 a canteen which lies within the limits of a certain municipal council which charges 8 percent of the assessed annual value of the property as rates has to pay quarterly rates of thousand 200 so that's quarterly cottony you have to pay thousands 200 what is the assists annual value of the canteen so quarterly value is this so what's the value for annual you multiplied by that's the 8 percent value annually so eight over hundred means this much 4,800 so we are asked to find out the persist annual value assessed annual value means you first find one part that means you divide by eight and 100% value is the total assists well 600 multiplied by 100 so you get six and four zeroes that means 60,000 rupees is the assessed and world Val question number five mr. Silva who owns the house assessed to be of annual value 30,000 rupees has rented it for a year to mr. Pereyra so what's the assessed value thirty thousand rupees and rented it for a year to mr. Pereyra the monthly rent charged by mr. Silva is three thousand so mr. Pereira is paying three thousand for a month the relevant provision council charges four percent of the assists annual value of the house as rates so four percent of the assessed value mr. Silva has to spend fifteen percent of the rent on maintenance how much of the rent is mr. Silva left with at the end of the year after after the relevant expenses are met so here 30% is the assessed value from that he has to pay 4% for the tax so for the 4% tax as the rates so first we will calculate the value value of the rates 30,000 in to 4% thousand two hundred and then how much he earns from this rent this is for a month for the year we need to multiply by 12 so rent charges is 3000 multiplied by 12 36,000 he is getting but he has to spend 15% of the rent on maintenance so what's the value for the maintenance for the maintenance you have to pay 15% so 36 thousands into 15% two zeros get cancelled out 360 x 15 10 and five five times zero five times six 30 15 plus three eighty so what's the value so you get five thousand four hundred so what's the total amount that he has to pay total amount five thousand four hundred and this thousand two hundred for tax altogether it's six thousand six hundred so the remaining amount the remaining amount is you you are getting thirty six thousand subtract six thousand six hundred what's the value for ten seven nine two remaining amount is twenty nine thousand four hundred question number six the value of a refrigerator which is being imported is forty thousand if the customs duty that has to be paid is twenty percent of the value of the item find the amount that has to be paid as duty so 20 percent of that value the value that you have to pays 0 0 this 0 get cancel out with this zero two times four thousand is eight thousand rupees push number seven if three thousand had to be played as customs duty when a camera worth twelve thousand was important what is the percentage that was charged as customs duty so here three thousand had to pay it for custom duty you asked to find out the percentage value so percentage value is equal to you have to pay three thousand four twelve thousand rupees as a percentage you multiply by hundred three zeroes three zeroes three times four hundred divided by four twenty-five percent you have to pay as their tax value push number eight the percentage charge as customs duty when a three-wheeler is important is fifty percent of its value if the value of the three-wheeler with the customs duty included is 450 thousand what is the value of the three-wheeler without the custom duty so this is with the custom duty if you buy four hundred rupees you have to pay a 150 so if this is one 450 you over hundred so this is with the tax so 150 represent 450,000 what about one hundred percent four hundred and fifty thousand divided by hundred fifty multiplied by 100 see you don't get canceled out five times three five times - three times here one three so you get 150 thousand multiplied by 2 that means 300 thousands rupees you have to pick question number nine if customs duty of twelve percent of the value of the items is charged when a stock of readymade garments worth fifty thousand is exported so what's the custom duty twelve percent what is the value of the stock of garments after the customs duty has been paid so they are charging twelve percent so if this is hundred you have to pay one hundred twelve so you can straightaway find out the value you have to pay fifty thousand multiplied by one hundred twelve and divided by one hundred two zeros get canceled out zero zero five times to 10 five times 1/5 plus one six five times one is five have to pay fifty six thousand rupees question number ten when a certain type of motorcycle is imported customs duty 15 percent of its value has to be paid the value of a motorcycle of this type which was imported is 175 thousand what is the value of the motorcycle after the customs duties pay if the cost is hundred you have to pay 115 so straightaway you can find out the value with the custom duty that's one hundred and seventy five thousand rupees multiplied by hundred fifteen divided by hundred so multiply one hundred and seventy-five with hundred fifty hundred ten five first multiplied by hundred multiplied by ten and then 5 5 times 5 25 two remaining I times 7 35 Plus 2 37 pi times 1 5 + 3 8 so when you act all together 9 9 + 7 16 9 + 7 16 + 5 21 so what's the value so you are getting here there's not the zero there 21250 that means two hundred one thousand two hundred fifty rupees and the second part at what price should the motorcycle be sold to make a profit of 10% so to get a profit you need to sell 410 if this is hundred so we'll use that one if it's hundred we have to sell it 410 so therefore if this is the price twenty thousand two hundred and one thousand two hundred and fifty multiplied by 110 divided by hundred to get 10% profit one zero one zero with these two zeros you have to multiply by 11 11 times 555 fired remaining eleven times - 22 + 527 - remaining yep 11 times 111 11 + 213 one remaining and here eleven times 222 so what's the price 220 1375 rupees if he wants he wants ten percent profit question number 11 the annual income of a certain individual is five hundred fifty thousand how much income tax does he have to pay according to the income tax rate implemented in year 2011 so can you remember first 500000 tax is free and for the next 500 thousand that's four percent then the next five hundred thousand eight percent 12 percent like that so we'll take first five hundred thousand off so this is with no tax you get another fifty thousand so for fifty thousand you have to pay 4% tax so fifty thousand into four percent of that two zeros get canceled out 4 times 5 20 another two zeros so you have to be two thousand rupees for this income tax question number 12 how much should a person whose annual income is 1 million eight hundred thousand pay as income tax according to table thirteen point one so first five hundred thousand no tax so we have to subtract that amount now for the next five hundred thousand you have to pay 4% tax so we will calculate four percent of five hundred thousand so 400 into five hundred thousand two zeros get cancelled out 4 times 5 20 and three more zeros so twenty thousand rupees then for the next 500,000 you have to pay 8% so this is 4 percent this is 8 percent so 8 percent of 500 thousand that's 40,000 rupees now further this 300,000 you have to pay 12 percent so 12 percent of 300,000 1 2 3 and 36 so you have to pay 36,000 for that then you want to calculate the total income tax so we have to add all three together you get 0 0 0 and then six and nine total amount is 96 thousand rupees question number 13 if a businessman paid an annual income tax 56 thousand rupees in 2012 according to the income tax rates implemented in 2011 what is his annual income now the text is given and you asked to find out the annual income now here we know that first 500 thousand you are not paying any amount any tax no tax then for the next 500 thousand you are paying 4% of that so we'll see what's 4% five hundred thousand we are getting twenty thousand but still this is more than that then we have to say when you subtract twenty thousand from that what you get this is thirty six thousand again now the next one is eight percent tax for another five hundred thousand now we'll see what is 8 percent value of five hundred thousand you are getting 40,000 now we found out this is forty thousand rupees but you got thirty six thousand rupees that means not another five hundred five hundred thousand so that's that should be less than that now we will find out the amount so the amount of calculating is 8 percent value for thirty six thousand so thirty six thousand you divide by 8 and multiply by 100 what's the value divided by four four times two four times nine nine thousand here divide by two again 4500 so multiply by hundred four five one two three four so four hundred fifty thousand so for this 80 plus eight percent you are getting only four hundred fifty thousand so the total of all these is the annual income so what's the annual income so I can add all together so the annual income is 1,450,000 so I can write this one as annual income adding five hundred thousand that's five hundred thousand again and four hundred fifty thousand 1 million four hundred fifty thousand rupees is the annual income question number 14 the monthly telephone charges of a certain household is thousand two hundred rupees if the VAT charge charges are ten percent what is the total value of the bill so first we can do finding that and adding to this amount or straightaway you can do ten percent value is on renting over hundred so how did we get hundred and ten with the text if you buy for one hundred you have to pay one hundred tip and if it's for one this is 110 over hundred so straightaway you get the value so zero zero get canceled out twelve times 0 0 12 times one twelve and twelve times 1/12 plus 130 so thousand three hundred twenty rupees is the total bill with the tax question number 15 the charges that had to be met by a person who imported a certain vehicle are as follows custom duty four hundred thousand the price is six hundred thousand and four charges everything there if vector 15% was charged on all these expenses how much did he have to pay in total for the vehicle so what's the total price first we need to find out the total price with all these cost you get when you add all three together these values you are getting 1 million 50,000 and you need to pay 15% for this as wet so we can straight to me find out if this is 100 you have to pay 115 so if if it's 1 115 4 divided by 100 so you need to find out so the expenses with there with the bat value is equal to 1 million 50 thousand multiplied by 115 divided by 2 zeroes get cancelled out and you have to multiply 1 0 5 0 0 multiplied by 100 and 1510 5 multiplied by hundred multiplied by by 10 you get with some out and multiply by 5 and then add it together you get 1 million 200 7,500 question number 16 that of 15% is added to the monthly water bill of a household if trataba pays a total of thousand seven hundred and twenty five as his monthly water bill find the value of the bill without the wax so what's the bet percentage fifteen percent if this is hundred you you're paying 150 if this is one part you're paying 115 over 100 so this is with the tax so how can you find out the amount without tax you do other way around so thousand seven hundred and twenty five you divided by 150 and multiplied by hundred will divide by five five times to ten for 15 five times three five times three 54:22 that's four and five and multiply by hundred you get 34 three four five zero zero divided by twenty three so we'll do long division 23 times 123 when you subtract you get one hundred and fifteen thousand one hundred fifteen 415 this is five five times three fifteen one remaining so eleven the value is thousand five hundred so the bill water bill without the tax is thousand five hundred now we'll see what is interest is when you borrow money from a bank or any financial institute you have to pay extra amount to recover the loan or when you invest money in a bag you are getting extra money from the back so those are called interest when a loan has been taken from an individual or an institution the extra amount that has to be paid when settling the loan after period of time is called the interest or when money has been deposited in a bank or some other financial institution for a period of time the extra amount that is received and the end of the period is also called the interest normally interest calculate and wali so we call that the annual interest rate the interest rate can be also given as monthly or semiannual if it's monthly you have to divide by 12 if you have given de and well interest rate if it's semiannual means you have to divide it by two sometimes you are given the rate in monthly or same language and also interest you can divide into two parts interest you can divide into two parts simple interest and compound interest if the interest is calculated only for the initial value because this is simple interest if you are considering all the values that's called compound interest so compound interest we are doing in grade 11 so what is simple interest calculating the interest only for the initial value so that's simple interest for the initial but now we will see the examples related to simple interest example number one it took a man two years to settle a loan worth five thousand rupees per owed at an annual simple interest rate of 10% so simple interest rate is given 10 percent and number of years for two years this is the rate annual rate is given and borrowed money is five thousand how much interest did he pay in total so first so five thousand rupees ten percent Interest ten over hundreds this is for one year this is for two years you have to multiply by two so interest is equal to this value so zero zero get cancelled out this zero get cancelled out with this one and two times five hundred is thousand rupees example number to find the total amount that cinahl has to pay to settle a loan in three months so months given that's three months if he borrowed 8,000 feet at a monthly simple interest rate of 2% so rate is given monthly so what's the total amount that channel has to pay a thousand multiplied by two percent of that value multiplied by three because oh it's for three months this is the interest to zeros get cancelled out three times - 6 6 times 8 48 so 480 rupees so what's the total amount with this interest total amount is amount plus the interest 8480 example number three how long will it take for a person who gave a loan of 10,000 rupees at an annual simple interest rate of 12 percent to receive an interest of 3600 so what's the loan amount 10,000 so first we'll find out if it's 10,000 what's the interest he has to pay so 10,000 interest is 10,000 into 12 percent two zeros get cancelled out 12 zero zero twelve that's 1200 rupees and then the total interest is these 3600 so this is for one year so you can find out the number of years is equal to number of years is equal to 3600 divided by thousand two hundred you get three so for three years he needs to take money to get three thousand six hundred as the interest value example number four if the simple interest that had to be paid for two years on alone 7500 was thousand two hundred so the interest is given thousand two hundred find the annual simple interest rate that was charged so you have to do other way round now the amount is given and interest is thousand two hundred the interest is for two years so what's the interest for one year you have to divide thousand two hundred by two you get six hundred rupees and you're paying six hundred and Whirley for 7,500 so what's the rate percentage rate is 600 for 7,500 and as a percentage you multiply by 100 to zeros get cancelled out / 3 3 times 2 3 times 2 6 & 5 so 25 times 4 4 times 2 8 percent example number 5 how many years after taking a loan of 25 thousand at an annual simple interest rate of 7.5% does a person have to pay a total amount of twenty eight thousand seven hundred and fifty to settle the low you can find out the interest by subtracting these two so interest is twenty eight thousand seven hundred and fifty minus twenty five thousand so what's the interest paid so what's the subtraction twenty eight thousand seven hundred and fifty subtract twenty five thousand you get three thousand seven hundred fifty rupees that's the total interest paid but what's the percentage the interest value for a year interest for a year is seven point five percent off twenty five thousand two zeroes get cancelled out so 1.5 x 10 you get 75 that means 75 times twenty-five so multiply 75 times twenty-five I'll do it here twenty and five five seven eight 1875 now we can find out how many years for that so number of years is equal to three thousand seven hundred and fifty divided by thousand eight hundred seventy-five this is twice of this so two years is the answer for this example example number six if the total amount that had to be paid after four months to settle a loan borrowed at a monthly simple interest rate of 1.5% was five thousand three hundred find the loan amount so first we'll find out what's the value for one month for four months you have to pay so one month is one point five for four months you have to multiply by four so if this is hundred rupees borrowed you have to pay one point five rupees four hundred rupees and for four months so four hundred rupees for four months what's the interest 1.5 into four you get six rupees now altogether what's the amount he has to be 106 so total amount for four months is six plus hundred that's 106 rupees now we know he has to pay five thousand three hundred rupees for the whole amount so that means 106 / hundred represent five thousand three hundred so we need to find out what is hundred percent so hundred percent value is five thousand three hundred divided by hundred six multiplied by 100 so when you do the calculations you are getting five times this you get five hundred and thirty so five this is 50 so 50 times 100 is five thousand rupees so the answer they ask that if the total amount this is with the interest find the loan amount is only five thousand rupees exercise 14.2 how much interest is received in three years when a loan of five thousand is given at an annual simple interest rate of 12 percent so the interest rate is 12% and the loan amount is five thousand for three years this is simple interest so interest is equal to the value multiplied by 12 percent twelve over hundred and you have to multiply by three because it's for three years zeros get canceled out three times 5 15 so 150 x twelve twelve times zero zero 12 two times five sixty twelve times one twelve plus six you get eighteen so what's the interest amount thousand eight hundred rupees second question a man deposits fifty thousand rupees in a bank at a monthly interest rate of 1.5 percent so the amount is fifty thousand monthly rate is 1.5 percent this is monthly rate if he withdraws the interest he receives monthly how much interest does he get in total during a period of six months so we'll calculate the interest for one year for one month and multiplied by 6 to get the interest for 6 months for one month 50,000 x 1.5 over hundred and for six months you multiply it by six 2 zeros get cancelled out so we'll first find one point five into six you get nine so nine times five hundred you get four thousand five hundred for six months question number three find a simple interest that has to be paid for one year and five months one year and five months on a loan of two thousand five hundred borrowed at a monthly rate three percent so we will first convert how many months are there one year twelve months and twelve plus five all together seventeen months are there so you asked to calculate the simple interest that has to be paid so here the amount simple interest is equal to the amount is two thousand five hundred with three percent monthly and how many months for seventeen months two zeros get canceled out three times 25 is 3 times 25 75 times 17 so we'll multiply 75 times 17 gen9 server you get seven times 535 7 times 7 49 + 350 1265 rupees for 17 months if a person who borrowed five hundred rupees settled alone in one year by paying back receipt 560 rupees find the annual interest rate that was charged so borrowed 500 rupees settle the loan by paying five hundred and sixty rupees find the annual interest rate so what's the interest paid interest paid is just subtract ting this value from here it's one 550 minus 500 that's sixty rupees so sixty rupees paid interest paid for five hundred so what's the annual rate interest rate percentage interest rate is the amount in of interest divided by the value of borrowed times hundred so you get five sixty divided by five twelve percent fifth one if a person who gave a loan of six thousand rupees at an annual simple interest rate received three thousand six hundred as interest for four years so this is the interest for four years what is the annual simple interest rate that was charged so this is for four years interest in that so what is the interest for one year interest for one year is 3600 divided by 4 you get nine hundred rupees so you have to pay nine hundred rupees for one year so what's the percentage interest rate so interest rate is equal to nine hundred for 6000 rupees in two hundred and then you get 3 times 2 or 3 times 3 2 times 5 so 5 times 3 15% interest rate question number 6 if a person who borrowed 600 rupees paid hundred thirty-five as interest so six hundred and 135 interest for one year this is for one year and three months one and three months find the monthly interest rate that was charged so here first we'll find out total number of months one year means twelve months plus 350 months for fifteen months paid one hundred thirty-five repeats as the interest for one month how much paid you're paying 135 divided by 15 five times three five times to ten seven you get nine nine rupees for one month so what's the monthly interest rate monthly percentage interest rate is nine four six hundred multiplied by 100 you get one point five percent question number seven if a person who gave a loan of eight thousand rupees received a total amount of nine thousand six hundred eighty at the end of two years it's two years find the annual simple interest rate was charged so what's the interest paid for two years interest for two years you can subtract this amount nine thousand six hundred eighty subtract eight thousand you get thousand six hundred and eighty so what's the interest for one year thousand six hundred and eighty divided by two look at eight hundred forty rupees so that's for one year so what's the percentage simple interest rate annual interest rate is 40 over eight hundred and forty over eight thousand multiplied by hundred so simplify you'll get 84 divided by 8 8 times 1 8 times 0 4 40 that's 5 so 10.5 as the percentage worth question number eight at what annual simple interest rate should alone of 5,000 rupees given to receive the same interest that is received when a loan of six thousand rupees is given at an annual simple interest rate of 8 percent so the interest is the same so we can find out the interest from this part so interest paid is six thousand into 8 over 100 you get 480 and here to get 480 as the interest then you can find out the interest rate so interest rate is 480 over five thousand now in two hundred percent zero zero get cancelled out 100 and divided by this you get five forty eight divided by five five times nine forty five four thirty that's six nine point six as the percentage value question number nine for what period of time should an interest of 540 rupees be paid on a loan of thousand five hundred rupees taken at an annual simple interest rate of 12 percent so you are asked to find out the period of time so we'll first find the interest value interest value is 12 percent of 1500 so when you multiply these two twelve plus five sixty sixty twelve into one 12 12 plus 6 18 280 rupees for one year that's the interest we need to find out how many years so number of years is equal to you paid 540 but within a year your paycheck paying 182 piece so what's the value three times this so you are paying for what's the period here three years question number ten in how many months will an interest of 420 rupees be earned on a loan of two thousand rupees given at a monthly simple interest rate of three percent so you are asking how many months are there so here first calculate the interest interest is two thousand rupees with three percent interest rate you are getting sixty rupees interest for a month but you paid 420 so there are four number of months is equal to 420 divided by sixty rupees you are getting seven months question number 11 after how long is a person who has taken a loan of six thousand at an annual simple interest rate of 18 percent able to settle the loan by paying back nine thousand two hundred forty so the loan is six thousand and you are paying nine thousand two hundred forty okay first we'll find out the interest for one year six thousand into eighteen percent zero six times eight forty eight for remaining six times one 6 plus 4 10 so thousand eighty rupees per year but you're paying this much so what's the interest in total total interest paid is nine thousand two hundred and forty minus six thousand so when you subtract you are getting three thousand two hundred and forty so you can find out how many years he needs to take to pay it back number of years is equal to three thousand two hundred and forty divided by thousand eighty so this is three times of this so that means three years it's the answer question number 12 after how long has a person to pay a total amount of five thousand to settle a load of 2,500 taken at an annual simple interest rate 10% so we'll first calculate the interest for one year interest for one year 2500 into 10% calculate that value you get 250 rupees what's the difference between these two that's the total interest paid 5,000 minus 2500 so total interest is 2500 rupees so how many years are there so number of days yes is equal to total is 2500 annual interest is 250 so when you divide you get 10 years as the answer question number 30 a person takes a loan of 5000 rupees promising to pay interest at a monthly simple interest rate of 5% so this is for Vermont how much does he have to pay in total to settle the loan in six months so what's the interest for one month five thousand multiplied by five percent and for six months you multiply this by 6 2 zeroes you get 6 times 5 30 30 times 550 and another zero so thousand five hundred rupees you have to pay for six months so this is the interest but we want to find out the total that he has to pay so total amount is you are adding this interest to the value borrow that's five thousand so the total is you are getting six thousand five hundred rupees question number 14 what is the total amount that has to be paid in three years to a settle a loan of eight thousand taken at an annual simple rate of 15% so total amount so for what's the interest for one year eight thousand multiplied by 15 over hundreds but we need for three years eight times three or 15 times three forty five forty five times eight three hundred and sixty and then another zero three thousand six hundred rupees for one for three years here only raise this one because I multiplied this by three and then what's the total amount that he has to pay with the interest three thousand six hundred plus the value borrowed eleven thousand six hundred rupees question number fifty calculate the loan amount if a total amount of three thousand one hundred rupees had to be paid in eight months to settle the loan taken at a monthly simple interest rate of 3% so this is the amount with the interest so the total amount is given so what's the interest so here 3% with the interest it's 3100 so first we have to find out what's the value without the interest here the interest rate is 3% so that means if this is 100% borrowed do you have to pay 3 rupees and this is for one month so hundred rupees for one month that's three rupees what what about 100 rupees for 8 months because it says for 8 months so 3 into 8 that's 24 rupees so that means if you are taking hundred you are paying 24 extra so with the interest you are paying 124 rupees if you take 100 rupees you are paying 124 rupees and then if this is other way around now you are paying 124 rupees to get 100 value but the value with the interest is 3100 for 3100 what's the what's the amount that you have to borrow 100 divided by 124 multiplied by 3100 so simplify this divided by 425 and 4 times 3 and 4 times 1 now 31 and 3100 this is 100 twenty-five times hundred the value is 2500 so you need to borrow two thousand five hundred rupees to pay three thousand 100 rupees in 8 months question number 16 a person takes a loan on annual simple interest promising to settle the loan in two years by paying five thousand rupees however he was only able to settle the loan in five years at which time he had to pay six thousand five hundred rupees now how many years he took extra he took three more years extra so when you take the difference that's for three years so three years interest is equal to six thousand five hundred minus five thousand one thousand five hundred what's the interest for one year one thousand five hundred divided by three so five hundred rupees now here for two years if the initial plan was to pay for two years so what's the interest for two years so interest for two years was five hundred into two is thousand rupees now the first part is calculate the interest he has to pay it for a year so that's this part that's the first part here and second part what was the amount he borrowed to do the next part you need this so he had to pay 5,000 but the interest for two years is thousand so the amount that he borrowed so what's the amount borrowed here 5,000 paid with the interest interest is thousand so you need to subtract 5,000 in a thousand you get four thousand rupees father for this one that's the amount that he borrowed now the third part asks what's the what was the annual simple interest rate and was simple interest rate is you're paying 500 per year Oh four thousand rupees into 100 percent so two zeros and with this one zero you get 50 divided by four fifty divided by 4 is 25 divided by 2 that's 12.5 percent question number 17 if a person took a loan receipt P for a period of two years at an annual simple interest rate of our our percent rate write down an expression for the interest he has to pay for a month first we'll find out interest per year so interest per year is equal to the amount taken is P into our percent this is per year interest per year is this much and this is PR over hundred that's the interest for a year interest per month interest per month is you have to divide this by 12 again so PR over thousand two hundred then the second part write down an expression for the total interest I that he has to pay for period of two years so in the second part we need 40 years we know the interest per year is this much so interest forty years is annual interest multiplied by interest for seniors is you can take the annual value this is for one year multiplied by T so what's the answer P R T over hundred is equal to AI but in books to read out easily it's given like our PT over hundred so if you know the initial value and the rate for annual charged and the number of years you can straight away calculate the interest for T years in from this formula then look at the third part calculate I using the expression in two above P is four thousand look at the question it's given P equals four thousand R equals eight percent and T equals five so we'll use the formula now I equals substitute to the formula eight is our P is four thousand and T is fine two zeros get cancelled out you're getting five times eight forty forty times 4000 four times four sixteen thousand six hundred rupees as the interest in this section we covered percentages and taxes and simple interest and in grade 11 we'll do compound interest and I'll teach you how to do compound interest formula