Home » Class 7 Maths » NCERT Solutions for Class 7 Maths Chapter 8 – Comparing Quantities

NCERT Solutions for Class 7 Maths Chapter 8 – Comparing Quantities

Exercise 8.1 : Solutions of Questions on Page Number : 157

Q1 : 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.

Q2 : 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 = 3/6 = 1/2
∴ For 24 students, number of computers required = 24 * 1/2= 12
Hence, 12 computers are required for 24 students.

Q3 : 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 = 570 /3 = 190 lakh
Population of U.P in 2 km2 area = 1660 lakh
Population of U.P in 1 km2 area = 1660 / 2 = 830 lakh

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

Exercise 8.2 : Solutions of Questions on Page Number : 164

Q1 : Convert the given fractional numbers to per cents.
(a) 1/ 8

(b) 5/4

(c) 3/ 40

(d) 2/7

(a) 1/ 8 (b) 5/4 (c)  3/ 40 (d) 2/7 Q2 : 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 Q3 : 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 .  Q4 : 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) Q5 : 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

Q6 : 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% Q7 : 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%

Q8 : 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.

Q9 : 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.

Q10 : 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.

Exercise 8.3 : Solutions of Questions on Page Number : 171

Q1 : 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%

Q2 : 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 = Q3 : 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 = Q4 : 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 = = %

Q5 : 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

Q6 : 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.

Q7 : (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 Q8 : 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

Q9 :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

Q10 : 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.

Q11 : If Meena gives an interest of Rs 45 for one year at 9% rate p.a.. What is the sum she has borrowed?  