NCERT Solutions Class 7 Maths Chapter 8

NCERT Solutions for Class 7 Mathematics Chapter 8

NCERT Solutions for Class 7th Mathematics Chapter 8 Comparing Quantities are available on Extramarks to encourage and motivate students with their preparation for this chapter. In NCERT Solutions Class 7 Mathematics Chapter 8, students will find detailed step-by-step solutions to all exercises given in Chapter 8 of their Class 7 NCERT Mathematics textbook. 

The important topics covered in NCERT Class 7 Mathematics Chapter 8 are as follows:

  •  Equivalent Ratios
  • Percentage and its uses
  • Converting Fraction Numbers to Percentage
  • Converting Decimals to Percentage
  • Converting Percentages to Fractions or Decimals
  • Converting Ratios to Percent
  • Increase or Decrease as Percent
  • Buying and Selling
  • Profit or Loss 
  • Simple Interest
  • Interest in Multiple Years

NCERT Solutions for Class 7 Mathematics Chapter 8 - Comparing Quantities

(Include NCERT Solutions for Class 7 Mathematics Chapter 8)

Access NCERT Solutions for Class 7 Mathematics Chapter 8 - Comparing Quantities

NCERT Solutions for Class 7 Mathematics Chapter 8 - Comparing Quantities

The quantitative relation between two quantities which reflects the relative size of both the quantities is what is covered in the chapter: comparing quantities. It is simply the means to compare any two given quantities.

In daily life, there are many occasions when we compare two quantities.

While comparing quantities, the ratio for two different comparisons must be the same. But there's a rule in comparing quantities that states if the unit of the two quantities is not the same, it cannot be compared. 

Some important facts covered in this chapter are: 

  • Various quantities that are of the same kind are compared using their ratios.
  • If two fractions are equal, their ratios are also equal.
  • When two ratios are equal, then the four quantities are in proportion.
  • Percentages are numerators of fractions with the denominator 100 and they are also a way of comparing quantities.
  • For conversion of a percentage into a decimal, you need to drop the sign of percentage and then shift the decimal point two places to the left.
  • For conversion of a fraction into a percentage, you need to multiply the fraction by 100 and write the "%" sign on the right of the number.
  • Profit = SP – CP (when SP > CP).
  • Loss = CP – SP (when CP > SP).
  • Profit or Loss per cent is always calculated on CP.
  • Money borrowed is known as the principal.
  • Simple interest = (P x R x T)/100
  • Amount = Principal + Interest

Ratio:

Comparison through ratio means to know "how many times one quantity is of the other", or to know "what part of one quantity is the other". 

The ratio of two numbers ‘b’ and ‘c’ (c ≠ 0) is b/c and it is denoted by b:c. A ratio in the simplest form is also known as the ratio in the lowest terms.

Note: To compare two quantities or to find the ratio of two quantities, the general rule remains the same i.e. their units must be the same.

Different ratios can also be compared by writing them as ‘like-fractions’.

To make your concepts more clear, you can  refer to the exercises in NCERT Solutions Class 7 Mathematics Chapter 8 from Extramarks.  

Equivalent Ratios:

As mentioned earlier, we can compare various ratios by converting them to like fractions. If the like fractions obtained are equal, then the given ratios are said to be equivalent.

Percentage:

Percentages are numerators of fractions having denominators as 100 which are used in comparing results. As mentioned earlier, the percentage is represented by "%" and it is expressed as parts of hundredths.

For example, 8 % means 8 out of 100. It is written as 8% = 8/100 = 0.08.

If the total is not a hundred, then we need to convert the fraction into an equivalent fraction with denominator 100.

Ratios To Percent:

Sometimes, the parts of a whole quantity are given in the form of ratios that we can convert into percentages. 

Note:  Here, by converting we mean to convert the increase or decrease in a quantity as a percentage of the initial amount as per the given question.

Profit Or Loss As A Percentage:

We know that the price of any item at which it is bought is called its cost price (CP) and the price at which it is sold is called its selling price (SP).

Note:

If CP < SP, then there is a profit in the monetary transaction, and Profit = SP – CP.

If CP > SP, then there is a loss in the monetary transaction and Loss = CP – SP.

The percentage of profit or loss is always calculated on the CP.

Simple Interest:

The money borrowed is known as the Principal amount. For using a bank's money, the borrower pays some extra money to the bank which is called Interest. The total money paid back with interest is known as the Amount.

Thus, Amount = Principal + Interest

Interest is generally given in per cent for a period for which the loan is taken. Generally, the rate of interest is expressed as a percentage per year or annum.

 So, Principal is denoted by P, Rate of interest by R, and Time by T.

Now,  simple interest, or Interest = (Principal x Rate x Time)/100, or I = PRT/100

NCERT Solutions for Class 7 Mathematics– 

You can access the NCERT Solutions for Class 7 Mathematics  from Extramarks and practise the questions from the link given below. 

NCERT Solutions for Class 7 Mathematics

In case you found the solutions of Class 7 Mathematics Chapter 8 useful and want to continue studying Mathematics through our website, you can click on the link below to find solutions for the other chapters. 

NCERT Solutions for Class 7

Extramarks  offers  multiple  benefits beyond what was presented to you through the conventional teaching methods. The solutions offered by Extramarks can  help you in the following ways:

  1. Engaging study material - The solutions of Mathematics Class 7 made available on our website are simple and easy to comprehend. As a result, you don't get confused, in fact, they are motivated to practise more sample test papers, and questions to improve their score. 
  2. Concepts made easier- Solving Mathematics questions through a study guide makes your mind actively involved in learning at a deeper level to understand better. 
  3. Important concepts emphasised and explained- As you will practice Mathematics with Extramarks' solutions, you’ll know key topics and highlight the main concepts of the chapter which will help you gain confidence and score good marks in your exams. 

Q.1 

Find the ratio of:a Rs 5 to 50 paise b 15 kg to 210 gc 9 m to 27 cm d 30 days to 36 hour

Ans

( a ) Rs 5 to 50 paise 1 ruppe=100 paise So, 5 rupee=500 paise So, Rs 5 50 paise = 500 50 = 10 1 Thus, the required ratio is 10:1 . ( b ) 15 kg to 210 g 1 kg=1000 g So, 15 kg=15000 g So, 15 kg 210 g = 15000 210 = 500 7 Thus, the required ratio is 500:7 . ( c ) 9 m to 27 cm 1 m=100 cm So, 9 m=900 cm So, 9 m 27 cm = 900 27 = 100 3 Thus, the required ratio is 100:3 . ( d ) 30 days to 36 hour 1 day=24 hours So, 30 days=720 hours So, 30 days 36 hour = 720 36 = 20 1 Thus, the required ratio is 20:1 . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaGaaeOuaiaabohacaqGGaGaaeynaiaabccacaqG0bGaae4Bai aabccacaqG1aGaaGimaiaabccacaqGWbGaaeyyaiaabMgacaqGZbGa aeyzaaqaaiaaxMaacaaIXaGaaeiiaiaabkhacaqG1bGaaeiCaiaabc hacaqGLbGaeyypa0JaaeymaiaabcdacaqGWaGaaeiiaiaabchacaqG HbGaaeyAaiaabohacaqGLbaabaGaae4uaiaab+gacaqGSaGaaeiiai aaysW7caqG1aGaaeiiaiaabkhacaqG1bGaaeiCaiaabwgacaqGLbGa eyypa0JaaeynaiaabcdacaqGWaGaaeiiaiaabchacaqGHbGaaeyAai aabohacaqGLbaabaGaae4uaiaab+gacaqGSaGaaeiiamaalaaabaGa aeOuaiaabohacaqGGaGaaGynaaqaaiaaiwdacaaIWaGaaeiiaiaabc hacaqGHbGaaeyAaiaabohacaqGLbaaaiabg2da9maalaaabaGaaGyn aiaaicdacaaIWaaabaGaaGynaiaaicdaaaGaeyypa0ZaaSaaaeaaca aIXaGaaGimaaqaaiaaigdaaaaabaGaaeivaiaabIgacaqG1bGaae4C aiaabYcacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabkhacaqGLb GaaeyCaiaabwhacaqGPbGaaeOCaiaabwgacaqGKbGaaeiiaiaabkha caqGHbGaaeiDaiaabMgacaqGVbGaaeiiaiaabMgacaqGZbGaaeiiam aaL4babaGaaeymaiaabcdacaqG6aGaaeymaaaacaGGUaaabaWaaeWa aeaacaqGIbaacaGLOaGaayzkaaGaaeiiaiaabgdacaqG1aGaaeiiai aabUgacaqGNbGaaeiiaiaabshacaqGVbGaaeiiaiaabkdacaqGXaGa aGimaiaabccacaqGNbaabaGaaeymaiaabccacaqGRbGaae4zaiabg2 da9iaabgdacaqGWaGaaeimaiaabcdacaqGGaGaae4zaaqaaiaabofa caqGVbGaaeilaiaabccacaqGXaGaaeynaiaabccacaqGRbGaae4zai abg2da9iaabgdacaqG1aGaaeimaiaabcdacaqGWaGaaeiiaiaabEga aeaacaqGtbGaae4BaiaabYcacaqGGaWaaSaaaeaacaaIXaGaaGynai aabccacaqGRbGaae4zaaqaaiaaikdacaaIXaGaaGimaiaabccacaqG Nbaaaiabg2da9maalaaabaGaaGymaiaaiwdacaaIWaGaaGimaiaaic daaeaacaaIYaGaaGymaiaaicdaaaGaeyypa0ZaaSaaaeaacaaI1aGa aGimaiaaicdaaeaacaaI3aaaaaqaaiaabsfacaqGObGaaeyDaiaabo hacaqGSaGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGYbGaaeyz aiaabghacaqG1bGaaeyAaiaabkhacaqGLbGaaeizaiaabccacaqGYb GaaeyyaiaabshacaqGPbGaae4BaiaabccacaqGPbGaae4Caiaabcca daqjEaqaaiaabwdacaqGWaGaaeimaiaabQdacaqG3aaaaiaac6caae aadaqadaqaaiaabogaaiaawIcacaGLPaaacaqGGaGaaeyoaiaabcca caqGTbGaaeiiaiaabshacaqGVbGaaeiiaiaabkdacaqG3aGaaeiiai aabogacaqGTbaabaGaaeymaiaabccacaqGTbGaeyypa0Jaaeymaiaa bcdacaqGWaGaaeiiaiaabogacaqGTbaabaGaae4uaiaab+gacaqGSa GaaeiiaiaabMdacaqGGaGaaeyBaiabg2da9iaabMdacaqGWaGaaeim aiaabccacaqGJbGaaeyBaaqaaiaabofacaqGVbGaaeilaiaabccada WcaaqaaiaaiMdacaqGGaGaaeyBaaqaaiaaikdacaaI3aGaaeiiaiaa bogacaqGTbaaaiabg2da9maalaaabaGaaGyoaiaaicdacaaIWaaaba GaaGOmaiaaiEdaaaGaeyypa0ZaaSaaaeaacaaIXaGaaGimaiaaicda aeaacaaIZaaaaaqaaiaabsfacaqGObGaaeyDaiaabohacaqGSaGaae iiaiaabshacaqGObGaaeyzaiaabccacaqGYbGaaeyzaiaabghacaqG 1bGaaeyAaiaabkhacaqGLbGaaeizaiaabccacaqGYbGaaeyyaiaabs hacaqGPbGaae4BaiaabccacaqGPbGaae4CaiaabccadaqjEaqaaiaa bgdacaqGWaGaaeimaiaabQdacaqGZaaaaiaac6caaeaadaqadaqaai aabsgaaiaawIcacaGLPaaacaqGGaGaae4maiaaicdacaqGGaGaaeiz aiaabggacaqG5bGaae4CaiaabccacaqG0bGaae4BaiaabccacaqGZa GaaeOnaiaabccacaqGObGaae4BaiaabwhacaqGYbaabaGaaeymaiaa bccacaqGKbGaaeyyaiaabMhacqGH9aqpcaqGYaGaaeinaiaabccaca qGObGaae4BaiaabwhacaqGYbGaae4CaaqaaiaabofacaqGVbGaaeil aiaabccacaqGZaGaaeimaiaabccacaqGKbGaaeyyaiaabMhacaqGZb Gaeyypa0Jaae4naiaabkdacaqGWaGaaeiiaiaabIgacaqGVbGaaeyD aiaabkhacaqGZbaabaGaae4uaiaab+gacaqGSaGaaeiiamaalaaaba GaaG4maiaaicdacaqGGaGaaeizaiaabggacaqG5bGaae4Caaqaaiaa iodacaaI2aGaaeiiaiaabIgacaqGVbGaaeyDaiaabkhaaaGaeyypa0 ZaaSaaaeaacaaI3aGaaGOmaiaaicdaaeaacaaIZaGaaGOnaaaacqGH 9aqpdaWcaaqaaiaaikdacaaIWaaabaGaaGymaaaaaeaacaqGubGaae iAaiaabwhacaqGZbGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqG GaGaaeOCaiaabwgacaqGXbGaaeyDaiaabMgacaqGYbGaaeyzaiaabs gacaqGGaGaaeOCaiaabggacaqG0bGaaeyAaiaab+gacaqGGaGaaeyA aiaabohacaqGGaWaauIhaeaacaqGYaGaaeimaiaabQdacaqGXaaaai aac6caaaaa@A847@

Q.2 

In a computer lab, there are 3 computers for every 6students.How many computers will be needed for 24students?

Ans

For 6 students, number of computers required=3 So, for 1 student, number of computers required= 3 6 = 1 2 Thus, for 24 students, number of computers required= 1 2 ×24 = 12 Therefore, 12 computers are needed for 24 students.

Q.3

Population of Rajasthan=570 lakhs andpopulation of UP=1660 lakhArea of Rajasthan= 3 lakh km2 andarea of UP = 2 lakh km2.i How many people are there per km2 in both these States?iiWhich State is less populated?

Ans

(i) Population of Rajasthan in 3 lakh km 2 =570 lakhs Population of Rajasthan in 1 lakh km 2 = 570 3 = 190 Population of UP in 2 lakh km 2 =1660 lakhs Population of UP in 1 lakh km 2 = 1660 2 = 830 (ii) From above data, clearly Rajasthan is less populated.

Q.4

Convert the given fractional numbers to per cents.(a)19 b54 c340 d27

Ans

(a) 1 8 = 1 8 × 100 100 = 1 8 ×100%=12.5% ( b ) 5 4 = 5 4 × 100 100 = 5 4 ×100%=125% ( c ) 3 40 = 3 40 × 100 100 = 3 40 ×100%=7.5% ( d ) 2 7 = 2 7 × 100 100 = 2 7 ×100%=28 4 7 %

Q.5 Convert the given decimal fractions to percents.
a. 0.65 b. 2.1 c. 0.02 d. 12.35

Ans

( a ) 0.65 =0.65×100%= 65×100 100 %=65% ( b ) 2.1 =2.1×100%= 21×100 10 %=210% ( c ) 0.02 =0.02×100%= 2×100 100 %=2% ( d ) 12.35 =12.35×100%= 1235×100 100 %=1235% MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaadaqadaqaaiaabggaaiaawIcacaGLPaaa caqGGaGaaGimaiaac6cacaqG2aGaaeynaaqaaiabg2da9iaaicdaca GGUaGaaGOnaiaaiwdacqGHxdaTcaaIXaGaaGimaiaaicdacaGGLaGa eyypa0ZaaSaaaeaacaaI2aGaaGynaiabgEna0kaaigdacaaIWaGaaG imaaqaaiaaigdacaaIWaGaaGimaaaacaGGLaGaeyypa0JaaGOnaiaa iwdacaGGLaaabaWaaeWaaeaacaqGIbaacaGLOaGaayzkaaGaaeiiai aabkdacaGGUaGaaeymaaqaaiabg2da9iaaikdacaGGUaGaaGymaiab gEna0kaaigdacaaIWaGaaGimaiaacwcacqGH9aqpdaWcaaqaaiaaik dacaaIXaGaey41aqRaaGymaiaaicdacaaIWaaabaGaaGymaiaaicda aaGaaiyjaiabg2da9iaaikdacaaIXaGaaGimaiaacwcaaeaadaqada qaaiaabogaaiaawIcacaGLPaaacaqGGaGaaGimaiaac6cacaaIWaGa aeOmaaqaaiabg2da9iaaicdacaGGUaGaaGimaiaaikdacqGHxdaTca aIXaGaaGimaiaaicdacaGGLaGaeyypa0ZaaSaaaeaacaaIYaGaey41 aqRaaGymaiaaicdacaaIWaaabaGaaGymaiaaicdacaaIWaaaaiaacw cacqGH9aqpcaaIYaGaaiyjaaqaamaabmaabaGaaeizaaGaayjkaiaa wMcaaiaabccacaqGXaGaaeOmaiaac6cacaqGZaGaaeynaaqaaiabg2 da9iaaigdacaaIYaGaaiOlaiaaiodacaaI1aGaey41aqRaaGymaiaa icdacaaIWaGaaiyjaiabg2da9maalaaabaGaaGymaiaaikdacaaIZa GaaGynaiabgEna0kaaigdacaaIWaGaaGimaaqaaiaaigdacaaIWaGa aGimaaaacaGGLaGaeyypa0JaaGymaiaaikdacaaIZaGaaGynaiaacw caaaaa@AD33@

Q.6 Estimate what part of the figures is coloured and hence find the percent which is coloured.

Ans

(i) From the figure, we observe that 1 part out of 4 is shaded, so its 1 4 . 1 4 × 100 100 = 1 4 ×100%=25% (ii) From the figure, we observe that 3 part out of 5 is shaded, so its 3 5 . 3 5 × 100 100 = 3 5 ×100%=60% (iii) From the figure, we observe that 3 part out of 8 is shaded, so its 3 8 . 3 8 × 100 100 = 3 8 ×100%=37.5% MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaaabaGa aeOraiaabkhacaqGVbGaaeyBaiaabccacaqG0bGaaeiAaiaabwgaca qGGaGaaeOzaiaabMgacaqGNbGaaeyDaiaabkhacaqGLbGaaeilaiaa bccacaqG3bGaaeyzaiaabccacaqGVbGaaeOyaiaabohacaqGLbGaae OCaiaabAhacaqGLbGaaeiiaiaabshacaqGObGaaeyyaiaabshacaqG GaGaaeymaiaabccacaqGWbGaaeyyaiaabkhacaqG0bGaaeiiaiaab+ gacaqG1bGaaeiDaiaabccacaqGVbGaaeOzaiaabccacaqG0aGaaeii aiaabMgacaqGZbGaaeiiaiaabohacaqGObGaaeyyaiaabsgacaqGLb GaaeizaiaabYcaaeaacaqGZbGaae4BaiaabccacaqGPbGaaeiDaiaa bohacaqGGaWaaSaaaeaacaaIXaaabaGaaGinaaaacaGGUaaabaWaaS aaaeaacaaIXaaabaGaaGinaaaacqGHxdaTdaWcaaqaaiaaigdacaaI WaGaaGimaaqaaiaaigdacaaIWaGaaGimaaaacqGH9aqpdaWcaaqaai aaigdaaeaacaaI0aaaaiabgEna0kaaigdacaaIWaGaaGimaiaacwca cqGH9aqpcaaIYaGaaGynaiaacwcaaeaacaqGOaGaaeyAaiaabMgaca qGPaGaaeiiaaqaaiaabAeacaqGYbGaae4Baiaab2gacaqGGaGaaeiD aiaabIgacaqGLbGaaeiiaiaabAgacaqGPbGaae4zaiaabwhacaqGYb GaaeyzaiaabYcacaqGGaGaae4DaiaabwgacaqGGaGaae4Baiaabkga caqGZbGaaeyzaiaabkhacaqG2bGaaeyzaiaabccacaqG0bGaaeiAai aabggacaqG0bGaaeiiaiaabodacaqGGaGaaeiCaiaabggacaqGYbGa aeiDaiaabccacaqGVbGaaeyDaiaabshacaqGGaGaae4BaiaabAgaca qGGaGaaeynaiaabccacaqGPbGaae4CaiaabccacaqGZbGaaeiAaiaa bggacaqGKbGaaeyzaiaabsgacaqGSaaabaGaae4Caiaab+gacaqGGa GaaeyAaiaabshacaqGZbGaaeiiamaalaaabaGaaG4maaqaaiaaiwda aaGaaiOlaaqaamaalaaabaGaaG4maaqaaiaaiwdaaaGaey41aq7aaS aaaeaacaaIXaGaaGimaiaaicdaaeaacaaIXaGaaGimaiaaicdaaaGa eyypa0ZaaSaaaeaacaaIZaaabaGaaGynaaaacqGHxdaTcaaIXaGaaG imaiaaicdacaGGLaGaeyypa0JaaGOnaiaaicdacaGGLaaabaGaaeik aiaabMgacaqGPbGaaeyAaiaabMcacaaMe8oabaGaaeOraiaabkhaca qGVbGaaeyBaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeOzaiaa bMgacaqGNbGaaeyDaiaabkhacaqGLbGaaeilaiaabccacaqG3bGaae yzaiaabccacaqGVbGaaeOyaiaabohacaqGLbGaaeOCaiaabAhacaqG LbGaaeiiaiaabshacaqGObGaaeyyaiaabshacaqGGaGaae4maiaabc cacaqGWbGaaeyyaiaabkhacaqG0bGaaeiiaiaab+gacaqG1bGaaeiD aiaabccacaqGVbGaaeOzaiaabccacaqG4aGaaeiiaiaabMgacaqGZb GaaeiiaiaabohacaqGObGaaeyyaiaabsgacaqGLbGaaeizaiaabYca aeaacaqGZbGaae4BaiaabccacaqGPbGaaeiDaiaabohacaqGGaWaaS aaaeaacaaIZaaabaGaaGioaaaacaGGUaaabaWaaSaaaeaacaaIZaaa baGaaGioaaaacqGHxdaTdaWcaaqaaiaaigdacaaIWaGaaGimaaqaai aaigdacaaIWaGaaGimaaaacqGH9aqpdaWcaaqaaiaaiodaaeaacaaI 4aaaaiabgEna0kaaigdacaaIWaGaaGimaiaacwcacqGH9aqpcaaIZa GaaG4naiaac6cacaaI1aGaaiyjaaaaaa@3382@

Q.7

Find:a 15% of 250          b 1% of 1 hourc 20% of Rs 2500         d 75% of 1 k

Ans

( a ) 15% of 250 = 15 100 ×250= 75 2 =37.5 ( b ) 1% of 1 hour 1 hour=60 minutes. So, 1% of 1 hour = 1 100 ×60= 6 10 = 3 5 ( c ) 20% of Rs 2500 = 20 100 ×2500=20×25=500 ( d ) 75% of 1 kg 1 kg=1000 g. So, 75% of 1 kg = 75 100 ×1000=75×10=750

Q.8

Find the whole quantity ifa 5% of it is 600. b 12% of it is 1080.c 40% of it is 500 km. d 70% of it is 14 minutese 8% of it is 40 litre

Ans

( a ) 5% of it is 600 is same as 5% of x is 600. 5 100 ×x=600 x= 600×100 5 =12000 ( b ) 12% of it is 1080 is same as 12% of x is 1080. 12 100 ×x=1080 x= 1080×100 12 =9000 ( c ) 40% of it is 500 km is same as 40% of x is 500km. 40 100 ×x=500 x= 500×100 40 =1250 ( d ) 70% of it is 14 minutes is same as 70% of x is 14minutes 70 100 ×x=14 x= 14×100 70 =20 ( e ) 8% of it is 40 litres is same as 8% of x is 40litres 8 100 ×x=40 x= 40×100 8 =500

Q.9

Convert given per cents to decimal fractions and also tofractions in simplest forms:a 25% b 150% c 20% d 5%

Ans

( a ) 25% = 25 100 = 1 4 =0.25 ( b ) 150% = 150 100 = 15 10 = 3 2 =1.5 ( c ) 20% = 20 100 = 2 10 = 1 5 =0.2 ( d ) 5% = 5 100 = 1 20 =0.05

Q.10

In a city, 30% are females, 40% are males and remainingare children. What percent are children?

Ans

Children=( 100( 30+40 ) )% =( 10070 )% =30%

Q.11

Out of 15,000 voters in a constituency, 60% voted.Find the percentage of voters who did not vote. Can younow find how many actually did not vote?

Ans

Percentage of voters who voted =60% Percentage of voters who did not vote=100%-60% =40% Number of voters who did not vote=40% of 15,000 = 40 100 ×15000 =6000 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGqbGaaeyzaiaabkhacaqGJbGaaeyz aiaab6gacaqG0bGaaeyyaiaabEgacaqGLbGaaeiiaiaab+gacaqGMb GaaeiiaiaabAhacaqGVbGaaeiDaiaabwgacaqGYbGaae4Caiaabcca caqG3bGaaeiAaiaab+gacaqGGaGaaeODaiaab+gacaqG0bGaaeyzai aabsgacaWLjaGaaGjbVlaaysW7caaMe8UaaGjbVlabg2da9iaaiAda caaIWaGaaiyjaiaaxMaaaeaacaqGqbGaaeyzaiaabkhacaqGJbGaae yzaiaab6gacaqG0bGaaeyyaiaabEgacaqGLbGaaeiiaiaab+gacaqG MbGaaeiiaiaabAhacaqGVbGaaeiDaiaabwgacaqGYbGaae4Caiaabc cacaqG3bGaaeiAaiaab+gacaqGGaGaaeizaiaabMgacaqGKbGaaeii aiaab6gacaqGVbGaaeiDaiaabccacaqG2bGaae4BaiaabshacaqGLb GaaGjbVlabg2da9iaabgdacaqGWaGaaeimaiaabwcacaqGTaGaaeOn aiaabcdacaqGLaaabaGaaCzcaiaaxMaacaWLjaGaaCzcaiaaxMaaca WLjaGaaCzcaiaaxMaacaaMe8UaaGjbVlaaysW7cqGH9aqpcaqG0aGa aeimaiaabwcaaeaacaqGobGaaeyDaiaab2gacaqGIbGaaeyzaiaabk hacaqGGaGaae4BaiaabAgacaqGGaGaaeODaiaab+gacaqG0bGaaeyz aiaabkhacaqGZbGaaeiiaiaabEhacaqGObGaae4BaiaabccacaqGKb GaaeyAaiaabsgacaqGGaGaaeOBaiaab+gacaqG0bGaaeiiaiaabAha caqGVbGaaeiDaiaabwgacqGH9aqpcaqG0aGaaeimaiaabwcacaqGGa Gaae4BaiaabAgacaqGGaGaaeymaiaabwdacaqGSaGaaeimaiaabcda caqGWaaabaGaaCzcaiaaxMaacaWLjaGaaCzcaiaaxMaacaWLjaGaaC zcaiaaysW7caaMe8UaaGjbVlaaysW7cqGH9aqpdaWcaaqaaiaaisda caaIWaaabaGaaGymaiaaicdacaaIWaaaaiabgEna0kaaigdacaaI1a GaaGimaiaaicdacaaIWaaabaGaaCzcaiaaxMaacaWLjaGaaCzcaiaa xMaacaWLjaGaaCzcaiaaysW7caaMe8UaaGjbVlaaysW7cqGH9aqpca aI2aGaaGimaiaaicdacaaIWaaaaaa@E379@

Q.12

Meeta saves 400 from her salary. If this is 10% of hersalary. What is her salay?

Ans

Let her salary be x. Then according to the question, we have 10% of x= 400 10 100 ×x=400 x= 400×100 10 =4000 Therefore Meeta’s salary is ₹ 4000

Q.13

A local cricket team played 20 matches in one season.It won 25% of them. How many matches did they win?

Ans

Since team played 20 matches, So, number of matches won=25% of 20 = 25 100 ×20 = 500 100 =5 So, number they won 5 matchces

Q.14

Tell what is the profit or loss in the following transactions.Also find profit per cent or loss per cent in each case.a Gardening shears bought for 250 and sold for 325.b A refrigerater bought for 12,000 and sold at 13,500.c A cupboard bought for 2,500 and sold at 3,000.d A skirt bought for 250 and sold at 150.

Ans

(a) Cost price=₹ 250 Selling price=₹ 325 Profit=325250 =75 Profit% = Profit Cost Price ×100 = 75 250 ×100 =30% (b) Cost price=₹ 12000 Selling price=₹ 13,500 Profit=135001200 =1500 Profit% = Profit Cost Price ×100 = 1500 12000 ×100 =12.5% (c) Cost price=₹ 2500 Selling price=₹ 3,000 Profit=30002500 =500 Profit% = Profit Cost Price ×100 = 500 2500 ×100 =20% (d) Cost price=₹ 250 Selling price=₹ 150 Loss=250150 =1000 Loss% = Loss Cost Price ×100 = 100 250 ×100 =40% MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabbIcaOiab bggaHjabbMcaPiabbccaGiabboeadjabb+gaVjabbohaZjabbsha0j abbccaGiabbchaWjabbkhaYjabbMgaPjabbogaJjabbwgaLjabg2da 9iabbcgaGjabbccaGiabbkdaYiabbwda1iabbcdaWaqaaiabbccaGi 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Q.15

Convert each part of the ratio to percentage:a 3:1        b2:3:5        c 1:4         d1: 2:5.

Ans

( a ) 3:1 Here total parts =3+1=4 1 st part= 3 4 = 3 4 ×100%=75% 2 nd part= 1 4 = 1 4 ×100%=25% ( b )2:3:5 Here total parts =2+3+5=10 1 st part= 2 10 = 2 10 ×100%=20% 2 nd part= 3 10 = 3 10 ×100%=30% 3 rd part= 5 10 = 5 10 ×100%=50% ( c ) 1:4 Here total parts =1+4=5 1 st part= 1 5 = 1 5 ×100%=20% 2 nd part= 4 5 = 4 5 ×100%=80% ( d )1: 2:5 Here total parts =1+2+5=8 1 st part= 1 8 = 1 8 ×100%=12.5% 2 nd part= 2 8 = 2 8 ×100%=25% 3 rd part= 5 8 = 5 8 ×100%=62.5% MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaamaabmaabaGa eeyyaegacaGLOaGaayzkaaGaeeiiaaIaee4mamJaeiOoaOJaeeymae dabaGaeeisaGKaeeyzauMaeeOCaiNaeeyzauMaeeiiaaIaeeiDaqNa ee4Ba8MaeeiDaqNaeeyyaeMaeeiBaWMaeeiiaaIaeeiCaaNaeeyyae MaeeOCaiNaeeiDaqNaee4CamNaeeiiaaIaeyypa0JaeG4mamJaey4k aSIaeGymaeJaeyypa0JaeGinaqdabaGaeGymaeZaaWbaaSqabeaacq qGZbWCcqqG0baDaaGccqqGGaaicqqGWbaCcqqGHbqycqqGYbGCcqqG 0baDcqGH9aqpdaWcaaqaaiabiodaZaqaaiabisda0aaacqGH9aqpda WcaaqaaiabiodaZaqaaiabisda0aaacqGHxdaTcqaIXaqmcqaIWaam cqaIWaamcqGGLaqjcqGH9aqpcqaI3aWncqaI1aqncqGGLaqjaeaacq aIYaGmdaahaaWcbeqaaiabb6gaUjabbsgaKbaakiabbccaGiabbcha WjabbggaHjabbkhaYjabbsha0jabg2da9maalaaabaGaeGymaedaba GaeGinaqdaaiabg2da9maalaaabaGaeGymaedabaGaeGinaqdaaiab gEna0kabigdaXiabicdaWiabicdaWiabcwcaLiabg2da9iabikdaYi abiwda1iabcwcaLaqaamaabmaabaGaeeOyaigacaGLOaGaayzkaaGa eeOmaiJaeiOoaOJaee4mamJaeiOoaOJaeeynaudabaGaeeisaGKaee yzauMaeeOCaiNaeeyzauMaeeiiaaIaeeiDaqNaee4Ba8MaeeiDaqNa eeyyaeMaeeiBaWMaeeiiaaIaeeiCaaNaeeyyaeMaeeOCaiNaeeiDaq Naee4CamNaeeiiaaIaeyypa0JaeGOmaiJaey4kaSIaeG4mamJaey4k aSIaeGynauJaeyypa0JaeGymaeJaeGimaadabaGaeGymaeZaaWbaaS qabeaacqqGZbWCcqqG0baDaaGccqqGGaaicqqGWbaCcqqGHbqycqqG YbGCcqqG0baDcqGH9aqpdaWcaaqaaiabikdaYaqaaiabigdaXiabic daWaaacqGH9aqpdaWcaaqaaiabikdaYaqaaiabigdaXiabicdaWaaa cqGHxdaTcqaIXaqmcqaIWaamcqaIWaamcqGGLaqjcqGH9aqpcqaIYa GmcqaIWaamcqGGLaqjaeaacqaIYaGmdaahaaWcbeqaaiabb6gaUjab bsgaKbaakiabbccaGiabbchaWjabbggaHjabbkhaYjabbsha0jabg2 da9maalaaabaGaeG4mamdabaGaeGymaeJaeGimaadaaiabg2da9maa laaabaGaeG4mamdabaGaeGymaeJaeGimaadaaiabgEna0kabigdaXi abicdaWiabicdaWiabcwcaLiabg2da9iabiodaZiabicdaWiabcwca LaqaaiabiodaZmaaCaaaleqabaGaeeOCaiNaeeizaqgaaOGaeeiiaa IaeeiCaaNaeeyyaeMaeeOCaiNaeeiDaqNaeyypa0ZaaSaaaeaacqaI 1aqnaeaacqaIXaqmcqaIWaamaaGaeyypa0ZaaSaaaeaacqaI1aqnae aacqaIXaqmcqaIWaamaaGaey41aqRaeGymaeJaeGimaaJaeGimaaJa eiyjauIaeyypa0JaeGynauJaeGimaaJaeiyjaucabaWaaeWaaeaacq qGJbWyaiaawIcacaGLPaaacqqGGaaicqqGXaqmcqGG6aGocqqG0aan cqqGGaaiaeaacqqGibascqqGLbqzcqqGYbGCcqqGLbqzcqqGGaaicq qG0baDcqqGVbWBcqqG0baDcqqGHbqycqqGSbaBcqqGGaaicqqGWbaC cqqGHbqycqqGYbGCcqqG0baDcqqGZbWCcqqGGaaicqGH9aqpcqaIXa qmcqGHRaWkcqaI0aancqGH9aqpcqaI1aqnaeaacqaIXaqmdaahaaWc beqaaiabbohaZjabbsha0baakiabbccaGiabbchaWjabbggaHjabbk haYjabbsha0jabg2da9maalaaabaGaeGymaedabaGaeGynaudaaiab g2da9maalaaabaGaeGymaedabaGaeGynaudaaiabgEna0kabigdaXi abicdaWiabicdaWiabcwcaLiabg2da9iabikdaYiabicdaWiabcwca LaqaaiabikdaYmaaCaaaleqabaGaeeOBa4MaeeizaqgaaOGaeeiiaa IaeeiCaaNaeeyyaeMaeeOCaiNaeeiDaqNaeyypa0ZaaSaaaeaacqaI 0aanaeaacqaI1aqnaaGaeyypa0ZaaSaaaeaacqaI0aanaeaacqaI1a qnaaGaey41aqRaeGymaeJaeGimaaJaeGimaaJaeiyjauIaeyypa0Ja eGioaGJaeGimaaJaeiyjaucabaWaaeWaaeaacqqGKbazaiaawIcaca GLPaaacqqGXaqmcqGG6aGocqqGGaaicqqGYaGmcqGG6aGocqqG1aqn aeaacqqGibascqqGLbqzcqqGYbGCcqqGLbqzcqqGGaaicqqG0baDcq qGVbWBcqqG0baDcqqGHbqycqqGSbaBcqqGGaaicqqGWbaCcqqGHbqy cqqGYbGCcqqG0baDcqqGZbWCcqqGGaaicqGH9aqpcqaIXaqmcqGHRa WkcqaIYaGmcqGHRaWkcqaI1aqncqGH9aqpcqaI4aaoaeaacqaIXaqm daahaaWcbeqaaiabbohaZjabbsha0baakiabbccaGiabbchaWjabbg gaHjabbkhaYjabbsha0jabg2da9maalaaabaGaeGymaedabaGaeGio aGdaaiabg2da9maalaaabaGaeGymaedabaGaeGioaGdaaiabgEna0k abigdaXiabicdaWiabicdaWiabcwcaLiabg2da9iabigdaXiabikda Yiabc6caUiabiwda1iabcwcaLaqaaiabikdaYmaaCaaaleqabaGaee OBa4MaeeizaqgaaOGaeeiiaaIaeeiCaaNaeeyyaeMaeeOCaiNaeeiD aqNaeyypa0ZaaSaaaeaacqaIYaGmaeaacqaI4aaoaaGaeyypa0ZaaS aaaeaacqaIYaGmaeaacqaI4aaoaaGaey41aqRaeGymaeJaeGimaaJa eGimaaJaeiyjauIaeyypa0JaeGOmaiJaeGynauJaeiyjaucabaGaeG 4mamZaaWbaaSqabeaacqqGYbGCcqqGKbazaaGccqqGGaaicqqGWbaC cqqGHbqycqqGYbGCcqqG0baDcqGH9aqpdaWcaaqaaiabiwda1aqaai abiIda4aaacqGH9aqpdaWcaaqaaiabiwda1aqaaiabiIda4aaacqGH xdaTcqaIXaqmcqaIWaamcqaIWaamcqGGLaqjcqGH9aqpcqaI2aGncq aIYaGmcqGGUaGlcqaI1aqncqGGLaqjaaaa@DB5C@

Q.16

The population of a city decreased from 25,000 to 24,500.Find the percentage decrease.

Ans

Initial population=25000 Final populaton=24500 Decrease=2500024500 =500 Decrease%= 500 25000 ×100 =2%

Q.17

Arun bought a car for 3,50,000. The next year, the pricewent up to 3,70,000. What was the Percentage of priceincrease?

Ans

Initial Price=₹ 3,50,000 Final Price =₹ 3,70,000 Increase =3,70,0003,50,000 = 20,000 Increase%= 20,000 3,50,000 ×100 =5 5 7 % MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabbMeajjab b6gaUjabbMgaPjabbsha0jabbMgaPjabbggaHjabbYgaSjabbccaGi abbcfaqjabbkhaYjabbMgaPjabbogaJjabbwgaLjabg2da9iabbcga GjabbccaGiabbodaZiabbYcaSiabbwda1iabbcdaWiabbYcaSiabbc daWiabbcdaWiabbcdaWaqaaiabbAeagjabbMgaPjabb6gaUjabbgga HjabbYgaSjabbccaGiabbcfaqjabbkhaYjabbMgaPjabbogaJjabbw gaLjabbccaGiabg2da9iabbcgaGjabbccaGiabbodaZiabbYcaSiab bEda3iabbcdaWiabbYcaSiabbcdaWiabbcdaWiabbcdaWaqaaiabbM eajjabb6gaUjabbogaJjabbkhaYjabbwgaLjabbggaHjabbohaZjab bwgaLjabbccaGiabbccaGiabbccaGiabbccaGiabg2da9iabbcgaGj aaysW7cqqGZaWmcqqGSaalcqqG3aWncqqGWaamcqqGSaalcqqGWaam cqqGWaamcqqGWaamcqGHsislcqqGGbaycaaMe8Uaee4mamJaeeilaW IaeeynauJaeeimaaJaeeilaWIaeeimaaJaeeimaaJaeeimaadabaGa aCzcaiaaxMaacqqGGaaicqqGGaaicqqGGaaicqGH9aqpcqqGGbayca aMe8UaeeOmaiJaeeimaaJaeeilaWIaeeimaaJaeeimaaJaeeimaada baGaeeiiaaIaeeysaKKaeeOBa4Maee4yamMaeeOCaiNaeeyzauMaee yyaeMaee4CamNaeeyzauMaeeyjauIaeyypa0ZaaSaaaeaacqaIYaGm cqaIWaamcqGGSaalcqaIWaamcqaIWaamcqaIWaamaeaacqaIZaWmcq GGSaalcqaI1aqncqaIWaamcqGGSaalcqaIWaamcqaIWaamcqaIWaam aaGaey41aqRaeGymaeJaeGimaaJaeGimaadabaGaeeiiaaIaeeiiaa IaeeiiaaIaeeiiaaIaeeiiaaIaeeiiaaIaeeiiaaIaeeiiaaIaeeii aaIaeeiiaaIaeeiiaaIaeeiiaaIaeeiiaaIaeeiiaaIaeeiiaaIaee iiaaIaeeiiaaIaeyypa0JaeGynauZaaSaaaeaacqaI1aqnaeaacqaI 3aWnaaGaeiyjaucaaaa@D7A1@

Q.18

I buy a T.V. for 10,000 and sell it at a profit of 20%. Howmuch money do I get for it?

Ans

We know that Profit%= Profit Cost price ×100 So, 20= Profit 10,000 ×100 = Profit 100× 100 × 100 Profit=20×100 =2000 Now, Profit=Selling priceCost price 2000=Selling price10000 Selling price=10000+2000 =12000 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabbEfaxjab bwgaLjabbccaGiabbUgaRjabb6gaUjabb+gaVjabbEha3jabbccaGi abbsha0jabbIgaOjabbggaHjabbsha0bqaaiabbcfaqjabbkhaYjab b+gaVjabbAgaMjabbMgaPjabbsha0jabbwcaLiabg2da9maalaaaba GaeeiuaaLaeeOCaiNaee4Ba8MaeeOzayMaeeyAaKMaeeiDaqhabaGa ee4qamKaee4Ba8Maee4CamNaeeiDaqNaeeiiaaIaeeiCaaNaeeOCai NaeeyAaKMaee4yamMaeeyzaugaaiabgEna0kabigdaXiabicdaWiab icdaWaqaaiabbofatjabb+gaVjabbYcaSaqaaiaaxMaacqaIYaGmcq aIWaamcqGH9aqpdaWcaaqaaiabbcfaqjabbkhaYjabb+gaVjabbAga MjabbMgaPjabbsha0bqaaiabigdaXiabicdaWiabcYcaSiabicdaWi abicdaWiabicdaWaaacqGHxdaTcqaIXaqmcqaIWaamcqaIWaamaeaa caWLjaGaaGjbVlaaysW7caaMe8UaaGjbVlabg2da9maalaaabaGaee iuaaLaeeOCaiNaee4Ba8MaeeOzayMaeeyAaKMaeeiDaqhabaGaeGym aeJaeGimaaJaeGimaaJaey41aq7aaqIaaeaacqaIXaqmcqaIWaamcq aIWaamaaaaaiabgEna0oaaKiaabaGaeGymaeJaeGimaaJaeGimaada aaqaaiaaysW7caaMe8UaeeiuaaLaeeOCaiNaee4Ba8MaeeOzayMaee yAaKMaeeiDaqNaeyypa0JaeeOmaiJaeeimaaJaey41aqRaeeymaeJa eeimaaJaeeimaadabaGaaCzcaiaaysW7caaMe8UaaGjbVlaaysW7cq GH9aqpcqqGGbaycaaMe8UaeeOmaiJaeeimaaJaeeimaaJaeeimaada baGaeeOta4Kaee4Ba8Maee4DaCNaeeilaWcabaGaaCzcaiaaysW7ca aMe8UaaGjbVlaaysW7caaMe8UaaGjbVlabbcfaqjabbkhaYjabb+ga VjabbAgaMjabbMgaPjabbsha0jabg2da9iabbofatjabbwgaLjabbY gaSjabbYgaSjabbMgaPjabb6gaUjabbEgaNjabbccaGiabbchaWjab bkhaYjabbMgaPjabbogaJjabbwgaLjabgkHiTiabboeadjabb+gaVj abbohaZjabbsha0jabbccaGiabbchaWjabbkhaYjabbMgaPjabboga JjabbwgaLbqaaiaaxMaacaaMe8UaaGjbVlaaysW7caaMe8Uaeeiyaa MaaGjbVlabbkdaYiabbcdaWiabbcdaWiabbcdaWiabg2da9iabbofa tjabbwgaLjabbYgaSjabbYgaSjabbMgaPjabb6gaUjabbEgaNjabbc caGiabbchaWjabbkhaYjabbMgaPjabbogaJjabbwgaLjabgkHiTiab bcgaGjaaysW7cqqGXaqmcqqGWaamcqqGWaamcqqGWaamcqqGWaamae aacaaMe8UaaGjbVlabbofatjabbwgaLjabbYgaSjabbYgaSjabbMga Pjabb6gaUjabbEgaNjabbccaGiabbchaWjabbkhaYjabbMgaPjabbo gaJjabbwgaLjabg2da9iabbcgaGjaaysW7cqqGXaqmcqqGWaamcqqG WaamcqqGWaamcqqGWaamcqGHRaWkcqqGGbaycaaMe8UaeeOmaiJaee imaaJaeeimaaJaeeimaadabaGaaCzcaiaaxMaacaaMe8UaaGjbVlaa ysW7caaMe8UaaGjbVlaaykW7caaMe8UaaGjbVlabg2da9iabbcgaGj aaysW7cqqGXaqmcqqGYaGmcqqGWaamcqqGWaamcqqGWaamaaaa@647E@

Q.19

Juhi sells a washing machine for 13,500. She loses 20% inthe bargain. What was the price at which she bought it?

Ans

Selling price = ₹ 13500 Loss % = 20% Let the cost price be x. Loss = 20% of x Cost price Loss = Selling price x20% of x=13500 x 20 100 ×x=13500 100x20x 100 =13500 80x 100 =13500 x= 13500×100 80 =16875 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabbofatjab bwgaLjabbYgaSjabbYgaSjabbMgaPjabb6gaUjabbEgaNjabbccaGi abbchaWjabbkhaYjabbMgaPjabbogaJjabbwgaLjabbccaGiabg2da 9iabbccaGiabbcgaGjabbccaGiabbgdaXiabbodaZiabbwda1iabic daWiabicdaWaqaaiabbYeamjabb+gaVjabbohaZjabbohaZjabbcca GiabcwcaLiabbccaGiabg2da9iabbccaGiabbkdaYiabicdaWiabcw caLaqaaiabbYeamjabbwgaLjabbsha0jabbccaGiabbsha0jabbIga OjabbwgaLjabbccaGiabbogaJjabb+gaVjabbohaZjabbsha0jabbc caGiabbchaWjabbkhaYjabbMgaPjabbogaJjabbwgaLjabbccaGiab bkgaIjabbwgaLjabbccaGiabdIha4jabc6caUaqaaiabgsJiCjabbc caGiabbYeamjabb+gaVjabbohaZjabbohaZjabbccaGiabg2da9iab bccaGiabbkdaYiabicdaWiabcwcaLiabbccaGiabb+gaVjabbAgaMj abbccaGiabdIha4bqaaiabboeadjabb+gaVjabbohaZjabbsha0jab bccaGiabbchaWjabbkhaYjabbMgaPjabbogaJjabbwgaLjabbccaGi abgkHiTiabbccaGiabbYeamjabb+gaVjabbohaZjabbohaZjabbcca Giabg2da9iabbccaGiabbofatjabbwgaLjabbYgaSjabbYgaSjabbM gaPjabb6gaUjabbEgaNjabbccaGiabbchaWjabbkhaYjabbMgaPjab bogaJjabbwgaLbqaaiaaxMaacaaMe8UaaGjbVlaaysW7caaMe8Uaee iEaGNaeyOeI0IaeGOmaiJaeGimaaJaeiyjauIaeeiiaaIaee4Ba8Ma eeOzayMaeeiiaaIaeeiEaGNaeyypa0JaeeiyaaMaaGjbVlabbgdaXi abbodaZiabbwda1iabbcdaWiabbcdaWaqaaiaaxMaacaWLjaGaeeiE aGNaeyOeI0YaaSaaaeaacqaIYaGmcqaIWaamaeaacqaIXaqmcqaIWa amcqaIWaamaaGaey41aqRaemiEaGNaeyypa0JaeGymaeJaeG4mamJa eGynauJaeGimaaJaeGimaadabaGaaCzcaiaaxMaadaWcaaqaaiabig daXiabicdaWiabicdaWiabdIha4jabgkHiTiabikdaYiabicdaWiab dIha4bqaaiabigdaXiabicdaWiabicdaWaaacqGH9aqpcqaIXaqmcq aIZaWmcqaI1aqncqaIWaamcqaIWaamaeaacaWLjaGaaCzcaiaaxMaa caaMe8UaaGjbVlaaysW7caaMe8+aaSaaaeaacqaI4aaocqaIWaamcq WG4baEaeaacqaIXaqmcqaIWaamcqaIWaamaaGaeyypa0JaeGymaeJa eG4mamJaeGynauJaeGimaaJaeGimaadabaGaaCzcaiaaxMaacaWLja GaaCzcaiaaysW7cqWG4baEcqGH9aqpdaWcaaqaaiabigdaXiabioda Ziabiwda1iabicdaWiabicdaWiabgEna0kabigdaXiabicdaWiabic daWaqaaiabiIda4iabicdaWaaaaeaacaWLjaGaaCzcaiaaxMaacaWL jaGaaGjbVlaaysW7caaMe8UaaGjbVlabg2da9iabbcgaGjaaysW7cq aIXaqmcqaI2aGncqaI4aaocqaI3aWncqaI1aqnaaaa@3634@

Q.20

i Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.ii If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick.

Ans

(i) Given ratio=10:3:12 Total=10+3+12 =25 Percentage of Carbon= 3 25 ×100 =12% (ii) Let the weight of the stick be x g So, 12% of x=3 12 100 ×x=3 x= 300 12 =25g MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabbIcaOiab bMgaPjabbMcaPiabbccaGiabbEeahjabbMgaPjabbAha2jabbwgaLj abb6gaUjabbccaGiabbkhaYjabbggaHjabbsha0jabbMgaPjabb+ga Vjabg2da9iabbgdaXiabbcdaWiabbQda6iabbodaZiabbQda6iabbg daXiabbkdaYaqaaiaaxMaacaaMe8UaaGjbVlaaysW7caaMe8UaaGjb VlaaysW7cqqGubavcqqGVbWBcqqG0baDcqqGHbqycqqGSbaBcqGH9a qpcqqGXaqmcqqGWaamcqGHRaWkcqqGZaWmcqGHRaWkcqqGXaqmcqqG YaGmaeaacaWLjaGaaCzcaiaaxMaacqGH9aqpcqqGYaGmcqqG1aqnae aacqqGqbaucqqGLbqzcqqGYbGCcqqGJbWycqqGLbqzcqqGUbGBcqqG 0baDcqqGHbqycqqGNbWzcqqGLbqzcqqGGaaicqqGVbWBcqqGMbGzcq qGGaaicqqGdbWqcqqGHbqycqqGYbGCcqqGIbGycqqGVbWBcqqGUbGB cqGH9aqpdaWcaaqaaiabiodaZaqaaiabikdaYiabiwda1aaacqGHxd aTcqaIXaqmcqaIWaamcqaIWaamaeaacaWLjaGaaCzcaiaaxMaacaWL jaGaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8Uaeyypa0JaeG ymaeJaeGOmaiJaeiyjaucabaGaeeikaGIaeeyAaKMaeeyAaKMaeeyk aKIaeeiiaaIaeeitaWKaeeyzauMaeeiDaqNaeeiiaaIaeeiDaqNaee iAaGMaeeyzauMaeeiiaaIaee4DaCNaeeyzauMaeeyAaKMaee4zaCMa eeiAaGMaeeiDaqNaeeiiaaIaee4Ba8MaeeOzayMaeeiiaaIaeeiDaq NaeeiAaGMaeeyzauMaeeiiaaIaee4CamNaeeiDaqNaeeyAaKMaee4y amMaee4AaSMaeeiiaaIaeeOyaiMaeeyzauMaeeiiaaIaeeiEaGNaee iiaaIaee4zaCgabaGaee4uamLaee4Ba8MaeeilaWIaeeiiaaIaeeym aeJaeeOmaiJaeeyjauIaeeiiaaIaee4Ba8MaeeOzayMaeeiiaaIaee iEaGNaeyypa0Jaee4mamdabaGaaCzcamaalaaabaGaeGymaeJaeGOm aidabaGaeGymaeJaeGimaaJaeGimaadaaiabgEna0kabdIha4jabg2 da9iabiodaZaqaaiaaxMaacaWLjaGaemiEaGNaeyypa0ZaaSaaaeaa cqaIZaWmcqaIWaamcqaIWaamaeaacqaIXaqmcqaIYaGmaaaabaGaaC zcaiaaxMaacaaMe8UaaGjbVlabg2da9iabikdaYiabiwda1iaaysW7 cqqGNbWzaaaa@052E@

Q.21 Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?

Ans

Cost price of book=₹ 275 Loss%=15 We have, Loss%= Loss Cost price ×100 15= Loss 275 ×100 Loss= 15×275 100 =41.25 Selling price=Cost priceLoss =27541.25 =₹ 233.75 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabboeadjab b+gaVjabbohaZjabbsha0jabbccaGiabbchaWjabbkhaYjabbMgaPj abbogaJjabbwgaLjabbccaGiabb+gaVjabbAgaMjabbccaGiabbkga Ijabb+gaVjabb+gaVjabbUgaRjabg2da9iabbcgaGjabbccaGiabbk daYiabbEda3iabbwda1aqaaiabbYeamjabb+gaVjabbohaZjabboha ZjabbwcaLiabg2da9iabbgdaXiabbwda1aqaaiabbEfaxjabbwgaLj abbccaGiabbIgaOjabbggaHjabbAha2jabbwgaLjabbYcaSaqaaiab bYeamjabb+gaVjabbohaZjabbohaZjabbwcaLiabg2da9maalaaaba GaeeitaWKaee4Ba8Maee4CamNaee4CamhabaGaee4qamKaee4Ba8Ma ee4CamNaeeiDaqNaeeiiaaIaeeiCaaNaeeOCaiNaeeyAaKMaee4yam MaeeyzaugaaiabgEna0kabigdaXiabicdaWiabicdaWaqaaiaaysW7 caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlabigdaXiabiwda1iabg2 da9maalaaabaGaeeitaWKaee4Ba8Maee4CamNaee4CamhabaGaeGOm aiJaeG4naCJaeGynaudaaiabgEna0kabigdaXiabicdaWiabicdaWa qaaiaaxMaacaaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7cqqG mbatcqqGVbWBcqqGZbWCcqqGZbWCcqGH9aqpdaWcaaqaaiabigdaXi abiwda1iabgEna0kabikdaYiabiEda3iabiwda1aqaaiabigdaXiab icdaWiabicdaWaaaaeaacaWLjaGaaGjbVlaaysW7caaMe8UaaCzcai aaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlabg2da9iabisda 0iabigdaXiabc6caUiabikdaYiabiwda1aqaaiabbofatjabbwgaLj abbYgaSjabbYgaSjabbMgaPjabb6gaUjabbEgaNjabbccaGiabbcha WjabbkhaYjabbMgaPjabbogaJjabbwgaLjabg2da9iabboeadjabb+ gaVjabbohaZjabbsha0jabbccaGiabbchaWjabbkhaYjabbMgaPjab bogaJjabbwgaLjabgkHiTiabbYeamjabb+gaVjabbohaZjabbohaZb qaaiaaxMaacaWLjaGaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaM c8Uaeyypa0JaeeiyaaMaaGjbVlabbkdaYiabbEda3iabbwda1iabgk HiTiabbcgaGjaaysW7cqqG0aancqqGXaqmcqqGUaGlcqqGYaGmcqqG 1aqnaeaacaWLjaGaaCzcaiaaysW7caaMe8UaaGjbVlaaysW7caaMe8 UaaGPaVlabg2da9iabbcgaGjabbccaGiabbkdaYiabbodaZiabboda Ziabb6caUiabbEda3iabbwda1aaaaa@2A0A@

Q.22 Find the amount to be paid at the end of 3 years in each case:
(a) Principal = ₹1,200 at 12% p.a.
(b) Principal = ₹7,500 at 5% p.a.

Ans

(a) Principal (P)=₹ 1200 Rate (R)=12% Time (T)=3 years S.I.= P×R×T 100 = 1200×12×3 100 =432 Amount =P+S.I. =1200+432=₹ 1632 (b) Principal (P) =₹ 7500 Rate (R)=5% Time (T)=3 years S.I.= P×R×T 100 = 7500×5×3 100 =1125 Amount =P+S.I. =7500+1125 =₹ 8625 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabbIcaOiab bggaHjabbMcaPaqaaiaaysW7cqqGqbaucqqGYbGCcqqGPbqAcqqGUb GBcqqGJbWycqqGPbqAcqqGWbaCcqqGHbqycqqGSbaBcqqGGaaicqqG OaakcqqGqbaucqqGPaqkcqGH9aqpcqqGGbaycqqGGaaicqqGXaqmcq qGYaGmcqqGWaamcqqGWaamaeaacaWLjaGaeeOuaiLaeeyyaeMaeeiD aqNaeeyzauMaeeiiaaIaeeikaGIaeeOuaiLaeeykaKIaeyypa0Jaee ymaeJaeeOmaiJaeeyjaucabaGaaCzcaiabbsfaujabbMgaPjabb2ga TjabbwgaLjabbccaGiabbIcaOiabbsfaujabbMcaPiabg2da9iabio daZiabbccaGiabbMha5jabbwgaLjabbggaHjabbkhaYjabbohaZbqa aiaaxMaacaWLjaGaaGjbVlaaykW7cqqGtbWucqqGUaGlcqqGjbqscq qGUaGlcqGH9aqpdaWcaaqaaiabbcfaqjabgEna0kabbkfasjabgEna 0kabbsfaubqaaiabigdaXiabicdaWiabicdaWaaaaeaacaWLjaGaaG jbVlaaykW7caWLjaGaaCzcaiabg2da9maalaaabaGaeGymaeJaeGOm aiJaeGimaaJaeGimaaJaey41aqRaeGymaeJaeGOmaiJaey41aqRaeG 4mamdabaGaeGymaeJaeGimaaJaeGimaadaaaqaaiaaxMaacaaMe8Ua aGPaVlaaxMaacaWLjaGaeyypa0JaeeiyaaMaeeiiaaIaeGinaqJaeG 4mamJaeGOmaidabaGaaCzcaiabbgeabjabb2gaTjabb+gaVjabbwha 1jabb6gaUjabbsha0jabbccaGiabg2da9iabbcfaqjabgUcaRiabbo fatjabb6caUiabbMeajjabb6caUaqaaiaaxMaacaWLjaGaaGjbVlaa ykW7caWLjaGaeyypa0JaeeiyaaMaaGjbVlabbgdaXiabbkdaYiabbc daWiabbcdaWiabgUcaRiabbcgaGjaaysW7cqqG0aancqqGZaWmcqqG YaGmcqGH9aqpcqqGGbaycqqGGaaicqqGXaqmcqqG2aGncqqGZaWmcq qGYaGmaeaacqqGOaakcqqGIbGycqqGPaqkaeaacqqGqbaucqqGYbGC cqqGPbqAcqqGUbGBcqqGJbWycqqGPbqAcqqGWbaCcqqGHbqycqqGSb aBcqqGGaaicqqGOaakcqqGqbaucqqGPaqkcqqGGaaicqGH9aqpcqqG GbaycqqGGaaicqqG3aWncqqG1aqncqqGWaamcqqGWaamaeaacaWLja GaeeOuaiLaeeyyaeMaeeiDaqNaeeyzauMaeeiiaaIaeeikaGIaeeOu aiLaeeykaKIaeyypa0JaeeynauJaeeyjaucabaGaaCzcaiabbsfauj abbMgaPjabb2gaTjabbwgaLjabbccaGiabbIcaOiabbsfaujabbMca Piabg2da9iabbodaZiabbccaGiabbMha5jabbwgaLjabbggaHjabbk haYjabbohaZbqaaiaaxMaacaWLjaGaaGjbVlaaysW7cqqGtbWucqqG UaGlcqqGjbqscqqGUaGlcqGH9aqpdaWcaaqaaiabbcfaqjabgEna0k abbkfasjabgEna0kabbsfaubqaaiabigdaXiabicdaWiabicdaWaaa aeaacaWLjaGaaCzcaiaaxMaacqGH9aqpdaWcaaqaaiabiEda3iabiw da1iabicdaWiabicdaWiabgEna0kabiwda1iabgEna0kabiodaZaqa aiabigdaXiabicdaWiabicdaWaaaaeaacaWLjaGaaCzcaiaaxMaacq GH9aqpcqqGGbaycqqGGaaicqaIXaqmcqaIXaqmcqaIYaGmcqaI1aqn aeaacaWLjaGaeeyqaeKaeeyBa0Maee4Ba8MaeeyDauNaeeOBa4Maee iDaqNaeeiiaaIaeyypa0JaeeiuaaLaey4kaSIaee4uamLaeeOla4Ia eeysaKKaeeOla4cabaGaaCzcaiaaxMaacaWLjaGaeyypa0Jaeeiyaa MaaGjbVlabbEda3iabbwda1iabbcdaWiabbcdaWiabgUcaRiabbcga GjaaysW7cqqGXaqmcqqGXaqmcqqGYaGmcqqG1aqnaeaacaWLjaGaaC zcaiaaxMaacqGH9aqpcqqGGbaycqqGGaaicqqG4aaocqqG2aGncqqG YaGmcqqG1aqnaaaa@6A86@

Q.23 What rate gives ₹280 as interest on a sum of ₹56000 in 2 years?

Ans

We know thatS.I=P×R×T100280=56000×R×2100R=280×10056000×2=0.25Therefore, the rate is 0.25%.

Q.24

If Meena gives an interest of 45 for one year at 9%rate p.a. What is the sum she has borrowed?

Ans

We know that S.I= P×R×T 100 So, we get 45= P×9×1 100 P= 45×100 9 =₹500 Therefore, she borrowed ₹ 500. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqedu uDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wD YLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYf gasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9 q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff 0dmeaabaqaciGacaGaaeqabaWaaqaafaaakqaabeqaaiabbEfaxjab bwgaLjabbccaGiabbUgaRjabb6gaUjabb+gaVjabbEha3jabbccaGi abbsha0jabbIgaOjabbggaHjabbsha0bqaaiabbofatjabb6caUiab bMeajjabg2da9maalaaabaGaeeiuaaLaey41aqRaeeOuaiLaey41aq RaeeivaqfabaGaeGymaeJaeGimaaJaeGimaadaaaqaaiabbofatjab b+gaVjabbYcaSiabbccaGiabbEha3jabbwgaLjabbccaGiabbEgaNj abbwgaLjabbsha0bqaaiabbsda0iabbwda1iabb2da9maalaaabaGa eeiuaaLaee41aCTaeeyoaKJaee41aCTaeeymaedabaGaeeymaeJaee imaaJaeeimaadaaaqaaiabbcfaqjabb2da9maalaaabaGaeeinaqJa eeynauJaee41aCTaeeymaeJaeeimaaJaeeimaadabaGaeeyoaKdaaa qaaiabb2da9iabbcgaGjaaysW7cqqG1aqncqqGWaamcqqGWaamaeaa cqqGubavcqqGObaAcqqGLbqzcqqGYbGCcqqGLbqzcqqGMbGzcqqGVb WBcqqGYbGCcqqGLbqzcqqGSaalcqqGGaaicqqGZbWCcqqGObaAcqqG LbqzcqqGGaaicqqGIbGycqqGVbWBcqqGYbGCcqqGYbGCcqqGVbWBcq qG3bWDcqqGLbqzcqqGKbazcqqGGaaicqqGGbaycqqGGaaicqqG1aqn cqqGWaamcqqGWaamcqqGUaGlaaaa@ADA9@

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FAQs (Frequently Asked Questions)
1. Give a summary of the topics covered in NCERT Solutions for Class 7 Mathematics Chapter 8?

Chapter 8 of NCERT Solutions for Class 7 Mathematics has 3 exercises. The topics covered in NCERT Solutions for Class 7 Mathematics Chapter 8 are as follows: 

8.1 – Introduction

8.2 – Equivalent Ratios

8.3 – Percentage – Another Way of Comparing Quantities

8.4 – Use of Percentages

8.5 – Prices Related to an Item or Buying or Selling

8.6 – Charge Given on Borrowed Money or Simple Interest

2. Define comparing quantities.

It is the quantitative relation between two quantities that reflects the relative size of both quantities. It is simply a means to compare the given two quantities.

3. What does PA stand for in comparing quantities?

The full form of PA in comparing quantities is Per Annum. It is a term used in a financial context to refer to a financial year.

4. What is a ratio?

A ratio is a comparison of two or more quantities having the same units. A ratio compares two quantities by division, with the number being divided termed as the antecedent and the divisor or number dividing termed as the consequent. The mathematical symbol used to denote ratio is “:” (which is read as “is to”).

5. Define equivalent ratios.

As mentioned before, for comparing two quantities, their units must be the same. In the case of ratios, two ratios can be compared by converting them into like fractions. If the two like fractions obtained are equal, we say that the two given ratios are equivalent ratios (which are obtained by dividing or multiplying both the antecedent and consequent of the given ratio by the same number).

6. How does Extramarks teach Comparing Quantities?

When teaching the comparison of two or more quantities, a student needs to understand the order of numbers and this is explained through the use of a number line. The useful tricks shared in   Extramarks Solutions will ultimately make the concepts easier for you.