Mathematics NCERT Grade 7, Chapter 8: Comparing Quantities: It is often required to compare two quantities in our daily life. They may be heights,weights, salaries, marks etc.
The chapter starts by explaining Equivalent Ratios.
• Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say the two given ratios are equivalent.
• Keeping things in proportion and getting solutions: If two ratios are equivalent then the four quantities are said to be in proportion. For example, the ratios 8 : 2 and 16 : 4 are equivalent therefore 8, 2, 16 and 4 are in proportion.
The next topic discussed is Percentage - Another Way of Comparing Quantities.
A way of comparing quantities is percentage.
Percentages are numerators of fractions with denominator 100.
• Meaning of Percentage
• Percentages when total is not hundred
• Converting Fractional Numbers to Percentage
• Converting Decimals to Percentage
• Converting Percentages to Fractions or Decimals
• Fun with Estimation
Emphasis will also be laid upon the Use of Percentages.
Percentages are widely used in our daily life:
• To find exact number when a certain percent of the total quantity is given.
• When parts of a quantity are given to us as ratios, it is seen how to convert them to percentages.
• The increase or decrease in a certain quantity can also be expressed as percentage.
• The profit or loss incurred in a certain transaction can be expressed in terms of percentages.
• While computing interest on an amount borrowed, the rate of interest is given in terms of percents.
• Interpreting Percentages
• Converting Percentages to “How Many”
• Ratios to Percents
• Increase or Decrease as Per Cent
Additionally, the Prices Related to an Item or Buying and Selling will also be discussed. Here questions related to money, cost price, selling price, profit, loss, interest etc will be taught.
• Profit or Loss as a Percentage
Lastly, the topic Charge Given on Borrowed Money or Simple Interest.
Amount = Principal + Interest.
• The money you borrow is known as sum borrowed or principal.
• Keeping this money for some time the borrower has to pay some extra money to the bank. This is known as Interest.
• Interest for Multiple Years
Each section is supplemented with ample examples and a detailed explanation.
This is a very important chapter not only from the examination point of view but also in handling the day to day life purchases.
All the important points of the discussion are summarized at the end of the chapter- Comparing Quantities.

Question 1:

Find the ratio of:

(a) Rs 5 to 50 paise (b) 15 kg to 210 g

(c) 9 m to 27 cm (d) 30 days to 36 hours

(a) Rs 5 to 50 paise

1 rupee = 100 paise

5 rupee = 500 paise

Hence, the required ratio is 10:1.

(b) 15 kg to 210 g

1 kg = 1000 g

15 kg = 15000 g

Hence, the required ratio is 500:7.

(c) 9 m to 27 cm

1 m = 100 cm

9 m = 900 cm

Hence, the required ratio is 100:3.

(d) 30 days to 36 hours

1 days = 24 hrs

30 days = 24 × 30 = 720 hrs

Hence, the required ratio is 20:1.

Question 2:

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

For 6 students, number of computers required = 3

∴ For 1 student, number of computers required =

∴ For 24 students, number of computers required == 12
Hence, 12 computers are required for 24 students.

Question 3:

Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.

Area of Rajasthan = 3 lakh km2 and area of UP = 2 lakh km2.

(i) How many people are there per km2 in both these States?

(ii) Which State is less populated?

(i) Population of Rajasthan in 3 km2 area = 570 lakh

Population of Rajasthan in 1 km2 area =

Population of U.P in 2 km2 area = 1660 lakh

Population of U.P in 1 km2 area = = 830 lakh

(ii) It can be observed that population per km2 area is lesser for Rajasthan. Therefore, Rajasthan is less populated.

Video Solution for comparing quantities (Page: 157 , Q.No.: 3)

NCERT Solution for Class 7 math - comparing quantities 157 , Question 3

Question 1:

Convert the given fractional numbers to per cents.

(a) (b)

(c) (d)

(a)

(b)

(c)

(d)

Question 2:

Convert the given decimal fractions to per cents.

(a) 0.65 (b) 2.1 (c) 0.02 (d) 12.35

(a) 0.65

(b)2.1

(c) 0.02

(d) 12.35

Question 3:

Estimate what part of the figures is coloured and hence find the per cent which is coloured.

(i) Here, 1 part out of 4 equal parts are shaded which represents the fraction .

(ii) Here, 3 parts out of 5 equal parts are shaded which represents the fraction .

(iii) Here, 3 parts out of 8 equal parts are shaded which represents the fraction.

Question 4:

Find:

(a) 15% of 250 (b) 1% of 1 hour

(c) 20% of Rs 2500 (d) 75% of 1 kg

(a)

(b) 1 hour = 60 minutes

(c)

(d)

Question 5:

Find the whole quantity if

(a) 5% of it is 600 (b) 12% of it is 1080

(c) 40% of it is 500 km (d) 70% of it is 14 minutes

(e) 8% of it is 40 litres

(a) 5% of x = 600

(b) 12% of x = Rs 1080

(c) 40% of x = 500 km

(d) 70% of x = 14 min

(e) 8% of x = 40 L

= 500 L

Question 6:

Convert given percents to decimal fractions and also to fractions in simplest forms:

(a) 25% (b) 150%

(c) 20% (d) 5%

(a) 25%

(b) 150%

(c) 20%

(d) 5%

Question 7:

In a city, 30% are females, 40% are males and remaining are children. What per cent are children?

It is given that 30% are females and 40% are males.

Children = (100 − 30 − 40) % = 30%

Question 8:

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

Percentage of voters who voted = 60%

Percentage of those who did not vote = 100% − 60% = 40%

Number of people who did not vote = 40% of 15000

Therefore, 6000 people did not vote.

Video Solution for comparing quantities (Page: 165 , Q.No.: 8)

NCERT Solution for Class 7 math - comparing quantities 165 , Question 8

Question 9:

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

Let Meeta’s salary be Rs x.

Given that,

10% of x = 400

x = 400 × 10 = Rs 4000

Therefore, Meeta’s salary is Rs 4000.

Question 10:

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

Number of games won = 25% of 20

Therefore, the team won 5 matches.

Question 1:

Tell what is the profit or loss in the following transactions. Also find profit

percent or loss percent in each case.

(a) Gardening shears bought for Rs 250 and sold for Rs 325.

(b) A refrigerator bought for Rs 12,000 and sold at Rs 13,500.

(c) A cupboard bought for Rs 2,500 and sold at Rs 3,000.

(d) A skirt bought for Rs 250 and sold at Rs 150.

(a) Cost price = Rs 250

Selling price = Rs 325

Profit = 325 − 250 = Rs 75

== 30%

(b) Cost price = Rs 12000

Selling price = Rs 13,500

Profit = 13500 − 12000 = Rs 1500

Profit % = = 12.5%

(c) Cost price = Rs 2500

Selling price = Rs 3000

Profit = 3000 − 2500 = Rs 500

Profit % == 20%

(d) Cost price = Rs 250

Selling price = Rs 150

Loss = 250 − 150 = Rs 100

Loss % = = 40%

Question 2:

Convert each part of the ratio to percentage:

(a) 3:1 (b) 2:3:5 (c) 1:4 (d) 1:2:5

(a) 3: 1

Total parts = 3 + 1 = 4

1st part

2nd part =

(b) 2: 3: 5

Total parts = 2 + 3 + 5 = 10

1st part =

2nd part =

3rd part =

(c) 1: 4

Total parts =1 + 4 = 5

1st part =

2nd part =

(d) 1: 2: 5

Total parts = 1 + 2 + 5 = 8

1st part =

2nd part =

3rd =

Question 3:

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

Initial population = 25000

Final population = 24500

Decrease = 500

% decrease =

Question 4:

Arun bought a car for Rs 3,50,000. The next year, the price went upto

Rs 3,70,000. What was the percentage of price increase?

Initial price = Rs 350000

Final price = Rs 370000

Increase = Rs 20000

% increase =

= %

Question 5:

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

Cost price = Rs 10000

Profit = 20% of 10000

= Rs 2000

Selling price = Cost price + Profit

= 10000 + 2000 = Rs 12,000
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Video Solution for comparing quantities (Page: 171 , Q.No.: 5)

NCERT Solution for Class 7 math - comparing quantities 171 , Question 5

Question 6:

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

Selling price = Rs 13500

Loss % = 20%

Let the cost price be x.

∴ Loss = 20% of x

Cost price − Loss = Selling price

= 16875

Therefore, she bought it for Rs 16875.
​​​

Video Solution for comparing quantities (Page: 171 , Q.No.: 6)

NCERT Solution for Class 7 math - comparing quantities 171 , Question 6

Question 7:

(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?

(i) Ratio of calcium, carbon, and oxygen = 10: 3: 12

As 10 + 3 +12 = 25,

Therefore, percentage of carbon = = 12%

(ii) Let the weight of the stick be x g.

12 % of x = 3

Question 8:

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

Cost price = Rs 275

Loss % = 15%

Loss = 15% of 275

Cost price − Loss = Selling price

275 − 41.25 = Selling price

Selling price = Rs 233.75

Question 9:

Find the amount to be paid at the end of 3 years in each case:

(a) Principal = Rs 1,200 at 12% p.a.

(b) Principal = Rs 7,500 at 5% p.a.

(a) Principal (P) = Rs 1200

Rate (R) = 12 % p.a.

Time (T) = 3 years

= Rs 432

Amount = P + S.I.

= 1200 + 432

= Rs 1632

(b) P = Rs 7500

R = 5% p.a.

T = 3 years

= Rs 1125

Amount = 7500 + 1125

= Rs 8625

Question 10:

What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?

Therefore, 0.25% gives Rs 280 as interest on the given sum.

Question 11:

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