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.

circle fraction

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%

Answer:

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

(b) 150%

Answer:

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

(c) 20%

Answer:

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

(d) 5%

Answer:

`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`



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