Comparing Quantities
Exercise 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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