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CBSE NCERT Solutions For Class 7 Mathematics Chapter 8

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Class- VII-CBSE-MathematicsComparing quantitiesCBSE NCERT Solutions for Class 7 Mathematics Chapter 8Back of Chapter QuestionsExercise 8.11.Find the ratio of:(a)(b)(c)(d) 5 to 50 paise15 kg to 210 g9 m to 27 cm30 days to 36 hoursSolution:(a)To find ratio, both values must be in same unit.Since, 1 100 paiseHence, 5 500 paise(b) 5Hence, the ratio of 5 to 50 paise 50 paise 500 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝To find ratio, both values must be in same unit.50 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 101 10: 1Since, 1 kg 1000 gHence, 15 kg 15000 g(c)15 kgHence, the ratio of 15 kg to 210 g 210 g 15000𝑔𝑔210𝑔𝑔To find ratio, both values must be in same unit. 5007 500: 7Since, 1 m 100cmHence, 9 π‘šπ‘š 900𝑐𝑐𝑐𝑐(d)9 π‘šπ‘šHence, the ratio of 9 π‘šπ‘š to 27 𝑐𝑐𝑐𝑐 27 𝑐𝑐𝑐𝑐 900 𝑐𝑐𝑐𝑐27 𝑐𝑐𝑐𝑐To find ratio, both values must be in same unit. 1003 100: 3Since, 1 day 24 hoursHence, 30 day 30 24 hours2.Hence, the ratio of 30 days to 36 hours 30 24 β„Žπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œ36 β„Žπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œ 72036 20: 1In a computer lab, there are 3 computers for every 6 students. How manycomputers will be needed for 24 students?Practice more on Comparing quantitiesPage - 1www.embibe.com

Class- VII-CBSE-MathematicsComparing quantitiesSolution:Given, for 6 students 3 computers are neede((d) 6 students need 3 computers3 1 student need 6 computer3 24 students need 6 24 12 computers3.Thus, 12 computers will be needed for 24 students.Population of Rajasthan 570 lakhs and population of UP 1660 lakhs. Areaof Rajasthan 3 lakh π‘˜π‘˜π‘šπ‘š2 and area of UP 2 lakh π‘˜π‘˜π‘šπ‘š2.(i)(ii)How many people are there per π‘˜π‘˜π‘šπ‘š2 in both these States?Which State is less populated?Solution:Given, Population of Rajasthan 570 lakhs and Area of Rajasthan 3 lakhπ‘˜π‘˜π‘šπ‘š2Population of UP 1660 lakhs and area of UP 2 lakh π‘˜π‘˜π‘šπ‘š2 .(i) Number of people per π‘˜π‘˜π‘šπ‘š2 π‘Žπ‘Žπ‘ŽTherefore, in Rajasthan number of people per π‘˜π‘˜π‘šπ‘š2 190 people per π‘˜π‘˜π‘šπ‘š2and, in UP number of people per π‘˜π‘˜π‘šπ‘š2 per π‘˜π‘˜π‘šπ‘š2(ii)Exercise 8.21.1660 π‘™π‘™π‘™π‘™π‘™π‘™β„Žπ‘ π‘ 2 π‘™π‘™π‘™π‘™π‘™π‘™β„Žπ‘ π‘  π‘˜π‘˜π‘˜π‘˜2570 π‘™π‘™π‘™π‘™π‘™π‘™β„Žπ‘ π‘ 3 π‘™π‘™π‘™π‘™π‘™π‘™β„Žπ‘ π‘  π‘˜π‘˜π‘˜π‘˜2 830 peopleHence, in Rajasthan 190 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝 π‘˜π‘˜π‘šπ‘š2 and in UP 830 people per π‘˜π‘˜π‘šπ‘š2are present.Since number of people per π‘˜π‘˜π‘šπ‘š2 is less in Rajasthan. Hence, Rajasthan isless populating (d)Convert the given fractional numbers to per cents.(a)(b)(c)(d)185434027Practice more on Comparing quantitiesPage - 2www.embibe.com

Class- VII-CBSE-MathematicsComparing quantitiesSolution:To convert a fraction into percentage, multiply it by 100.(a)(b)(c)(d)2.11Hence, 8 8 100% 55252% 12.5%Hence, 4 4 100% 125%33Hence, 40 40 100% 22Hence, 7 7 100% 3042007% 7.5%4% 28 7 %Convert the given decimal fractions to per cents.(a)(b)(c)(d)0.652.10.0212.35Solution:To convert a decimal fraction to per cents, multiply it by 100.(a)(b)(c)(d)3.Hence, 0.65 0.65 100% 65%Hence, 2.1 2.1 100% 210%Hence, 0.02 0.02 100% 2%Hence, 12.35 12.35 100% 1235%Estimate what part of the figures is coloured and hence find the per cent which iscoloured(i)(ii)Practice more on Comparing quantitiesPage - 3www.embibe.com

Class- VII-CBSE-MathematicsComparing quantities(iii)Solution:(i)In the figure, there is total 4 part where coloured part is 1. We can clearly see that1coloured part is 4.1 Percentage of coloured part 4 100% 25%(ii)In the figure, there is total 5 part where coloured part is 3. We can clearly see that3coloured part is 5.3 Percentage of coloured part 5 100% 60%(iii)Practice more on Comparing quantitiesPage - 4www.embibe.com

Class- VII-CBSE-MathematicsComparing quantitiesIn the figure, there is total 8 part where coloured part is 3. We can clearly see that3coloured part is 8.4.33 Percentage of coloured part 8 100% 2 25% 37.5%Find:(a)(b)(c)(d)15% of 2501% of 1 hour20% of 250075% of 1 kgSolution:(a)(b)(c)(d)5.1515% of 250 100 250 37.511% of 1 hour 100 (60 60) seconds 36 seconds(60 60)seconds][ 1hour 2020% of 2500 100 2500 5007575% of 1 kg 100 1000𝑔𝑔 750𝑔𝑔 [ 1 kg 1000g]Find the whole quantity if(a)(b)(c)(d)(e)5% of it is 600.12% of it is 1080.40% of it is 500 π‘˜π‘˜π‘˜π‘˜.70% of it is 14 minutes.8% of it is 40 litres.Solution:Let the whole quantity be π‘₯π‘₯.(a)Given, 5% of π‘₯π‘₯ 600Practice more on Comparing quantitiesPage - 5www.embibe.com

Class- VII-CBSE-MathematicsComparing quantities5 π‘₯π‘₯ 600100600 100 π‘₯π‘₯ 5 π‘₯π‘₯ 12000(b)Hence, the whole quantity is 12000.Given, 12% of π‘₯π‘₯ 108012 π‘₯π‘₯ 1080100 1080 100 π‘₯π‘₯ 12 π‘₯π‘₯ 9000(c)Hence, the whole quantity is 9000.Given, 40% of π‘₯π‘₯ 500 π‘˜π‘˜π‘˜π‘˜ 40 π‘₯π‘₯ 500 π‘˜π‘˜π‘˜π‘˜100 π‘₯π‘₯ 500 100π‘˜π‘˜π‘˜π‘˜40 π‘₯π‘₯ 1250 π‘˜π‘˜π‘˜π‘˜(d)Hence, the whole quantity is 1250 π‘˜π‘˜π‘˜π‘˜.Given, 70% of π‘₯π‘₯ 14 minutes70 π‘₯π‘₯ 14 minutes10014 100 π‘₯π‘₯ minutes70 π‘₯π‘₯ 20 minutes(e)Hence, the whole quantity is 20 minutes.Given, 8% of π‘₯π‘₯ 40 litres8 100 π‘₯π‘₯ 40 litres π‘₯π‘₯ 40 1008litres π‘₯π‘₯ 500 litresHence, the whole quantity is 500 litres.Practice more on Comparing quantitiesPage - 6www.embibe.com

Class- VII-CBSE-Mathematics6.Comparing quantitiesConvert given per cents to decimal fractions and also to fractions in 7.25125% 100 4 0.25(b)Hence, decimal fraction of 25% is 0.25 and fraction in simplest form of125% is 4.(c)Hence, decimal fraction of 150% is 1.5 and fraction in simplest form of3150% is 2.(d)Hence, decimal fraction of 20% is 0.2 and fraction in simplest form of120% is 5.1503150% 100 2 1.520120% 100 5 0.2515% 100 20 0.05Hence, decimal fraction of 5% is 0.05 and fraction in simplest form of15% is 20.In a city, 30% are females, 40% are males and remaining are children. What percent are children?Solution:Given, percentage of females 30%Percentage of males 40%Total percentage of females and males (30 40) % 70%Percentage of children Total percentage – Percentage of males and females 100% – 70% 30%8.Hence, 30% are children.Out of 15,000 voters in a constituency, 60% vote((d) Find the percentage ofvoters who didPractice more on Comparing quantitiesPage - 7www.embibe.com

Class- VII-CBSE-MathematicsComparing quantitiesnot vote. Can you now find how many actually did not vote?Solution:Given, total number of voters 15,000Percentage of voters who voted 60%Percentage of candidates who did not vote (100 – 60) % 40%Actual voters, who did not vote 40% of 1500040 100 15000 60009.Hence, 6,000 voters did not vote.Meeta saves 4000 from her salary. If this is 10% of her salary. What is hersalary?Solution:Let Meeta’s salary be π‘₯π‘₯.Given, 10% of π‘₯π‘₯ 400010 π‘₯π‘₯ 40001004000 100 π‘₯π‘₯ 10 π‘₯π‘₯ 4000010.Hence, Meeta’s salary is 40000.A local cricket team played 20 matches in one season. It won 25% of them. Howmany matches did they win?Solution:Given,Number of matches played by cricket team 20Percentage of matches won by team 25%Hence, total matches won by them 25% of 20 25 20100 5Hence, they won 5 matches.Practice more on Comparing quantitiesPage - 8www.embibe.com

Class- VII-CBSE-MathematicsComparing quantitiesExercise 8.31.Tell what is the profit or loss in the following transactions. Also find profit percent or loss per cent in each case.(a)(b)(c)(d)Gardening shears bought for 250 and sold for 325.A refrigerator bought for 12,000 and sold at 13,500.A cupboard bought for 2,500 and sold at 3,000.A skirt bought for 250 and sold at 150.Solution:(a)Cost price for Gardening shears is 250.Selling price for Gardening shears is 325.Since, SP CPThus, there is a profit.Profit 𝑆𝑆𝑆𝑆 𝐢𝐢𝐢𝐢 Profit 325 250 Profit 75Also, we know that, Profit % 75 Profit % 250 100%ProfitCP 100% profit % 30%(b)Hence, profit 75 and Profit % 30%.Cost price for refrigerator is 12000.Selling price for refrigerator is 13500.Since, 𝑆𝑆𝑆𝑆 𝐢𝐢𝐢𝐢Thus, there is a profit.Profit 𝑆𝑆𝑆𝑆 𝐢𝐢𝐢𝐢 Profit 13500 12000 Profit 1500Also, we know that, Profit % 1500 Profit % 12000 100%Practice more on Comparing quantitiesProfitCPPage - 9 100www.embibe.com

Class- VII-CBSE-MathematicsComparing quantities profit % 12.5%(c)Hence, profit 1500 and Profit % 12.5%.Cost price for cupboard is 2500.Selling price for cupboard is 3000.Since, 𝑆𝑆𝑆𝑆 𝐢𝐢𝐢𝐢Thus, there is a profit.Profit 𝑆𝑆𝑆𝑆 𝐢𝐢𝐢𝐢 Profit 3000 2500 Profit 500Also, we know that, Profit % 500 Profit % 2500 100ProfitCP 100 profit % 20%(d)Hence, profit 500 and Profit% 20%.Cost price for skirt is 250.Selling price for skirt is 150.Since, 𝐢𝐢𝐢𝐢 𝑆𝑆𝑆𝑆Thus, there is a loss.Loss 𝐢𝐢𝐢𝐢 𝑆𝑆𝑆𝑆 Loss 250 150 Loss 100Also, we know that, Loss % 100 Loss % 250 100LossCP 100 Loss % 40%2.Hence, Loss 100 and Loss% 40%.Convert each part of the ratio to percentage:(a)(b)(c)3 12 3 51 4Practice more on Comparing quantitiesPage - 10www.embibe.com

Class- VII-CBSE-Mathematics(d)Comparing quantities1 2 5Solution:(a)Given ratio is 3 1Total part is 3 1 4.Therefore, the first part of ratio to percentage (b)1The second part of ratio to percentage 4Given ration is 2 3 5Therefore, the first part of ratio to percentage (c)The third part of ratio to percentage Given ration is 1 4531010Given ration is 1 2 545Total part is 1 2 5 8.3.The third part of ratio to percentage 5810 100% 20%2815 100% 20% 100% 80%Therefore, the first part of ratio to percentage The second part of ratio to percentage 2 100% 50%Therefore, the first part of ratio to percentage (d) 100% 75% 100% 30%Total part is 1 4 5.The second part of ratio to percentage 4 100% 25%Total part is 2 3 5 10.The second part of ratio to percentage 318 100% 12.5% 100% 25% 100% 62.5%The population of a city decreased from 25,000 to 24,500. Find the percentagedecrease.Solution:Given, the decreased population of a city from 25,000 to 24,500.Hence, original population 25,000Final population 24,500Practice more on Comparing quantitiesPage - 11www.embibe.com

Class- VII-CBSE-MathematicsComparing quantitiesDecrease in population original population final population 25,000 24,500 500Percentage decrease 50025000 2%4. 100%Decrease in populationoriginal population 100%Hence, the percentage decrease in population of the city is 2%.Arun bought a car for 3,50,000. The next year, the price went upto 3,70,000.What was the percentage of price increase?Solution:Increased in price of a car from 3,50,000 to 3,70,000.Initial price 3,50,000Final price 3,70,000Increase in 20,000.price Finalprice InitialTherefore, percentage increase in price 20000 350000 100%5 5 %75.price 3,70,000 – 3,50,000 ΌπΌπΌπΌ 𝑖𝑖𝑖𝑖 ΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 100%5Hence, the percentage of price increase is 5 7 %.I buy a T.V. for 10,000 and sell it at a profit of 20%. How much money do I getfor it?Solution:Given, the cost price of T.V. 10,000Profit percent 20%We know that, Profit% Profit Profit profit% ‘π‘π‘π‘100𝐢𝐢𝐢𝐢 100%20 10000100 Profit 2000Since, Selling price ((C) P. ProfitPractice more on Comparing quantitiesPage - 12www.embibe.com

Class- VII-CBSE-MathematicsComparing quantities SP 10,000 2,000 12,0006.Hence, he gets 12000 on selling his T.V.Juhi sells a washing machine for 13,500. She loses 20% in the bargain. Whatwas the price at which she bought it?Solution:Given, selling price of washing machine 13,500Loss percent 20%Let the cost price of washing machine be π‘₯π‘₯We know that, Loss% Loss Loss 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿% ΆπΆπΆπΆ100 10020 π‘₯π‘₯100Since, 𝑆𝑆𝑆𝑆 𝐢𝐢𝐢𝐢 – Loss20 π‘₯π‘₯1001 13500 π‘₯π‘₯ π‘₯π‘₯54 13500 π‘₯π‘₯5 13500 π‘₯π‘₯ π‘₯π‘₯ 13500 54 π‘₯π‘₯ 168757.Hence, the cost price of washing machine is 16,875.(i)(ii)Chalk contains calcium, carbon and oxygen in the ratio 10 3 12. Findthe percentage of carbon in chalk.If in a stick of chalk, carbon is 3 𝑔𝑔, what is the weight of the chalk stick?Solution:(i)Given, ratio 10 3 12Therefore, total part 10 3 12 253Part of carbon 253Percentage of carbon part in chalk 25 100% 12%Practice more on Comparing quantitiesPage - 13www.embibe.com

Class- VII-CBSE-Mathematics(ii)Comparing quantitiesQuantity of carbon in chalk stick 3 𝑔𝑔Let the weight of chalk stick be π‘₯π‘₯ 𝑔𝑔. 12% of π‘₯π‘₯ 312 π‘₯π‘₯ 31003 100 π‘₯π‘₯ 25 g12 8.Hence, the weight of chalk stick is 25 g.Amina buys a book for 275 and sells it at a loss of 15%. How much does shesell it for?Solution:Given, CP of book is 275.Loss% 15%We know that, Loss% Loss Loss 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿% 0𝐢𝐢𝐢𝐢 10015 275100 Loss 41.25Therefore, 𝑆𝑆. 𝑃𝑃. 𝐢𝐢. 𝑃𝑃. – Loss S. P. 275 41.25 S. P. 233.759.Thus, she sells the book for 233.75.Find the amount to be paid at the end of 3 years in each case:(a)(b)Principal 1,200 π‘Žπ‘Žπ‘Žπ‘Ž 12% 𝑝𝑝. π‘Žπ‘Ž.Principal 7,500 π‘Žπ‘Žπ‘Žπ‘Ž 5% 𝑝𝑝. π‘Žπ‘Ž.Solution:(a)Given, 𝑃𝑃 1200𝑇𝑇 3 years𝑅𝑅 12% 𝑝𝑝. π‘Žπ‘Ž.We know that, S. I Practice more on Comparing quantitiesP R T100Page - 14www.embibe.com

Class- VII-CBSE-Mathematics S. I. Comparing quantities1200 12 3100 S. I. 432Also, amount principal S.I. Amount 1200 432 Amount 1632(b)Hence, amount to be paid at the end of 3 years is 1632.Given, 𝑃𝑃 7500𝑇𝑇 3 years𝑅𝑅 5% 𝑝𝑝. π‘Žπ‘Ž.We know that, S. I S. I. P R T1007500 5 3100 S. I. 1125Also, amount principal S.I. Amount 7500 1125 Amount 8,62510.Hence, amount to be paid at the end of 3 years is 8,625.What rate gives 280 as interest on a sum of 56,000 in 2 years?Solution:Given, 𝑃𝑃 56000𝑇𝑇 2 years𝑆𝑆. 𝐼𝐼. 280Let rate be π‘Ÿπ‘Ÿ% 𝑝𝑝. π‘Žπ‘Ž.We know that, S. I P R T10056000 π‘Ÿπ‘Ÿ 2100280 100 r 56000 2 280 r 0.25% p. ((a)Practice more on Comparing quantitiesPage - 15www.embibe.com

Class- VII-CBSE-Mathematics11.Comparing quantitiesHence, rate 0.25% per annum.If Meena gives an interest of 45 for one year at 9% rate p.a. What is the sum shehas borrowed?Solution:Given, 𝑅𝑅 9% 𝑝𝑝. π‘Žπ‘Ž.𝑇𝑇 1 year𝑆𝑆. 𝐼𝐼. 45Let the sum she has borrowed be π‘₯π‘₯.We know that, S. I 45 π‘₯π‘₯ π‘₯π‘₯ 9 1100P R T10045 1009 1 π‘₯π‘₯ 500Hence, she has borrowed 500. Practice more on Comparing quantitiesPage - 16www.embibe.com

Class- VII-CBSE-Mathematics Comparing quantities . Practice more on Comparing quantities . Page - 1 . www.embibe.com . CBSE NCERT Solutions for Class 7 Mathematics Chapter 8 . Back of Chapter Questions . Exercise 8.1 . 1. Find the ratio of: (a) 5 to 50 paise (b) 15 kg to 2