# Comparing Quantities

## Exercise 8.2

Question 1: Convert the given fractional numbers to per cents.

(a) 1/8

Answer: 1/8 xx 100 = 12.5%

(b) 5/4

Answer: 5/4 xx 100 = 125%

(c) (3)/(40)

Answer: (3)/(40) xx 100 = 7.5%

(d) 2/7

Answer: 2/7 xx 100 = 28.57%

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

(a) 0.65

Answer: 0.65 xx 100 = 65%

(b) 2.1

Answer: 2.1 × 100 = 210%

(c) 0.02

Answer: 0.02 × 100 = 2%

(d) 12.35

Answer: 12.35 xx 100 = 1235%

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

Answer: (i) 25% (ii) 60% (ii) 37.5%

Question 4: Find:

(a) 15% of 250

Answer: (250 xx 15)/(100) = 37.5

(b) 1% of 1 hour

Answer: Let us first convert 1 hour into seconds

1 hr = 60 xx 60 = 3600 second

3600 xx 1% = (3600 xx1)/(100) = 36 second

(c) 20% of Rs. 2500

Answer: (2500 xx20)/(100) = Rs. 500

(d) 75% of 1 kg

Answer: Let us first convert 1 kg into g

1 kg = 1000 g

(1000 xx 75)/(100) = 750 g

Question 5: Find the whole quantity if

(a) 5% of it is 600.

Answer: Let us assume the whole quantity = x

x\xx(5)/(100)=600

Or, x=(600xx100)/(5)=12000

(b) 12% of it is Rs. 1080.

Answer: Let us assume the whole quantity = x

x\xx(12)/(100)=1080

Or, x=(1080xx100)/(12)=9000

(c) 40% of it is 500 km.

Answer: Let us assume the whole quantity = x

x\xx(40)/(100)=500

Or, x=(500xx100)/(40)=1250 km

(d) 70% of it is 14 minutes.

Answer: Let us assume the whole quantity = x

x\xx(70)/(100)=14

Or, x=(14xx100)/(70)=20 min

(e) 8% of it is 40 litres.

Answer: Let us assume the whole quantity = x

x\xx(8)/(100)=40

Or, x=(40xx100)/(8)=500 liter

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

(a) 25%

25%=(25)/(100)=1/4

(b) 150%

150%=(150)/(100)=3/2=1\1/2

(c) 20%

20%=(20)/(100)=1/5

(d) 5%

5%=(5)/(100)=(1)/(20)

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

Answer: Total = 100, females = 30%, males = 40% and children = ?

Or, 30% + 40% + children = 100%

Or, 70% + children = 100%

Or, children = 100% - 70% = 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?

Answer: Total = 100%, voted = 60% not voted = ?

Or, 60% + Did not vote = 100%

Or, Did not vote = 100% - 60% = 40%

Number of people who did not vote:

=15000xx40%

=15000xx(40)/(100)=6000

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

Answer: Meeta’s salary can be calculated as follows:

(400xx100)/(10)=Rs. 4000

Alternate Method: When saving is Rs. 10 then salary is Rs. 100.

Hence, when saving is Rs. 1 then salary is 100/10

Hence, when saving is Rs. 400 then salary is

(400xx100)/(10)=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?

Answer: Number of matches won can be calculated as follows:

20xx25%=20xx(25)/(100)=5`