**Comparing Quantities**

**Exerci****se 8.2**

1). Convert the given fractional numbers to per cents.

(a) ^{1}/_{8} (b) ^{5}/_{4}

(c) ^{3}/_{40} (d) ^{2}/_{7}

Solution:

(a) ^{1}/_{8}

(b) ^{5}/_{4}

(c) ^{3}/_{40}

(d) ^{2}/_{7}

2). Convert the given decimal fractions to per cents.

(a) 0.65 (b) 2.1

(c) 0.02 (d) 12.35

Solution:

(a) 0.65

0.65 = ^{65} / _{100}

= 65 %

(b) 2.1

2.1 = ^{21}/_{10} = 210/100

= 210 %

(c) 0.02

0.002 = ^{2}/_{1000} = ^{0.2} / 100

= 0.2 %

(d) 12.35

12.35 = ^{1235}/_{100} = 1235%

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

Solution:

(i)

(ii)

(iii)

4). Find:

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

(c) 20% of ₹ 2500 (d) 75% of 1 kg

Solution:

(a) 15% of 250

(b) 1% of 1 hour

(c) 20% of ₹ 2500

(d) 75% of 1 kg

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.

Solution:

(a) 5% of it is 600.

Let the whole quantity be *x*

5% of *x* = 600

^{(5 X x)}/_{100} = 600

*x* = ^{(600 X 100)}/_{5}

*x* = ^{60000} /_{5}

*x* = 12000

(b) 12% of it is ₹1080.

Let the whole quantity be *x*

12 % of *x* = 1080

^{(12 X x)}/_{100} = 1080

*x* = ^{(1080 X 100)}/_{12}

*x* = ^{108000}/_{12}

*x* = 9000

(c) 40% of it is 500 km.

Let the whole quantity be *x*

40% of *x* = 500 km

^{(40 X x)}/_{100} = 500

*x* = ^{(500 X 100)}/_{40}

*x* = ^{50000} /_{40}

*x* = 1250 Km

(d) 70% of it is 14 minutes.

Let the whole quantity be *x*

70% of *x* = 14

^{(70 X x)}/_{100} = 14

*x* = ^{(14 X 100)}/_{70}

*x* = ^{1400}/_{70}

*x* = 20

(e) 8% of it is 40 litres.

Let the whole quantity be *x*

8% of *x* = 40

^{(8 X x)}/_{100} = 40

*x* = ^{(40 X 100)}/_{8}

*x* = ^{4000} /_{8}

*x* = 500

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

(a) 25% (b) 150% (c) 20% (d) 5%

Solution:

(a) 25% (b) 150%

(c) 20% (d) 5%

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

% of females = 30

% of males = 40

% of children= ?

Total % of population = 100

% of children = 100 – (% of females + % of males)

= 100 – (30 + 40)

= 100 – 70

= 30

Ans: % of children = 30

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?

Total voters = 15,000

% voted = 60

% persons not voted = 100 – 60 = 40

Number of persons not voted = 15000 X 40%

= 15000 X 40 / 100

= 150 X 40

= 6000

Ans: Number of persons not voted = 6000

9). Meeta saves ₹4000 from her salary. If this is 10% of her salary. What is her salary?

Let the salary of Meeta be *x*

Saving % = 10

Savings amount = ₹ 4000

4000 = 10% of *x*

4000 = ^{(10 X }^{x}^{)} /_{100}

*x* = ^{(4000 X 100)} / _{10}

*x *= ^{400000} / _{10}

= 40000

Ans: Meeta’s salary = ₹ 40000

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

Total matches played = 20

Won % = 25

Number of matches won = 25% of 20

= ^{(25 X 20)} / _{100}

= ^{500} / _{100}

= 5

Ans: number of matches won = 5.

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