NCERT Solutions: Comparing Quantities- 1 Notes | Study Mathematics (Maths) Class 7 - Class 7

Exercise 8.1 

Question 1:  Find the ratio of:
(a) Rs5 to 50 paise    
(b) 15 kg to 210 g
(c) 9 m to 27 cm    
(d) 30 days to 36 hours

Answer 1: To find ratios, both quantities should be in same unit.

(a) Rs 5 to 50 paise
⇒  5 x 100 paise to 50 paise    [∴ Rs 1 = 100 paise]
⇒  500 paise to 50 paise

Thus, the ratio is = 500/50 = 10/1 = 10 : 1

(b) 15 kg to 210 g
⇒ 15 x 1000 g to 210 g    [∵ 1kg = 1000 g]
⇒ 15000 g to 210 g
Thus, the ratio is = 15000/210 = 500/7 = 500:7

(c) 9 m to 27 cm
⇒  9 x 100 cm to 27 cm     [∵ 1m = 100 cm]
⇒  900 cm to 27 cm

Thus, the ratio is = 900/27 = 100/3 = 100:3

(d) 30 days to 36 hours
⇒  30 x 24 hours to 36 hours    [∵ 1 day = 24 hours]
⇒  720 hours to 36 hours

Thus, the ratio is = 720/36 = 20/1 = 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? 

Answer 2: 
∵ 6 students need = 3 computers

∵ 1 student needs = 3/6 computers

∵ 24 students need = 

Thus, 12 computers will be needed for 24 students.

Question 3: Population of Rajasthan = 570 lakhs and population of U.P. = 1660 lakhs. Area of Rajasthan = 3 lakh km² and area of U.P. = 2 lakh km². 

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

(ii) Which state is less populated? 

Answer 3: 

(ii) Rajasthan is less populated.

Exercise 8.2

Question 1: Convert the given fractional numbers to percent: 

(a) 1/8
(b) 5/4
(c) 3/40
(d) 2/7

Answer 1:

Question 2: Convert the given decimal fractions to per cents: 

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

Answer 2: 

Question 3: Estimate what part of the figures is coloured and hence find the percent which is coloured. 

Answer 3: (i) Coloured part = 1/4

 ∴ Percent of coloured part = 
(ii) Coloured part = 3/5
∴ Percent of coloured part

(iii) Coloured part = 3/8

∴ Percent of coloured part
= 37.5%

Question 4: Find: 

(a) 15% of 250 

(b) 1% of 1 hour 

(c) 20% of 2500 

(d) 75% of 1 kg 

Answer 4: (a) 15% of 250 

(b) 1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60] seconds

(c) 20% of Rs 500 
(d) 75% of 1 kg = 75% of 1000 g

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 

Answer 5: Let the whole quantity be x in given questions:

Question 6: Convert given per cents to decimal fractions and also to fractions in simplest forms: 

(a) 25% 

(b) 150% 

(c) 20% 

(d) 5% 

Answer 6: 

Question 7: In a city, 30% are females, 40% are males and remaining are children. What percent are children? 

Answer 7: 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%
Hence, 30% are children.

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? 

Answer 8: Total voters = 15,000

Percentage of voted candidates = 60%
Percentage of not voted candidates = 100 - 60 = 40%
Actual candidates, who did not vote = 40% of 15000 

Hence, 6,000 candidates did not vote.

Question 9: Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary? 

Answer 9: Let Meera's salary be Rs x.

Now, 10% of salary = Rs 400
⇒ 10% of x = Rs 400

Hence, Meera's salary is Rs 4,000.

Question 10: A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win? 

Answer 10: Number of matches played by cricket team = 20

Percentage of won matches = 25%
Total matches won by them = 25% of 20

Hence, they won 5 matches.