Class 7 Comparing Quantities Ex 7.1

Question 1. Convert the given fractional numbers to percent.
(a) \(1\over8\)

Solution:-

\(1\over8\) × 100 %

= 12.5%

(b) \(5\over4\)

Solution:-

= \(5\over4\) × 100 %

= 125%

(c) \(3\over40\)

Solution:-

= \(3\over40\) × 100 %

= \(15\over2\) %

= 7.5%

(d) \(2\over7\)

Solution:-

\(2\over7\) × 100 %

= \(200\over7\) %

=28\(4\over7\) %

Question 2. Convert the given decimal fraction to percent.

(a) 0.65

Solution:-

0.65= \(65\over100\)

Multiply by 100 and put the percent sign %

= \(65\over 100\) × 100

= 65%

(b) 2.1

Solution:-

2.1= \(21\over10\)

Multiply by 100 and put the percent sign %.

= \(21\over 10\) × 100

=210%

(c) 0.02

Solution:-

0.02 = \(2\over100\)

Multiply 100 and put the percent sign %.

= \(2\over100\) × 100

= 2%

(d) 12.35

Solution:-

12.35 = \(1235\over100\)

Multiply by 100 and put the percent sign %.

= \(1235\over 100\) × 100

= 1235%

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

Solution:-
(i)

It is represented by a fraction =  \(1 \over 4\)

= \(1 \over 4\) × 100

= 25%

Hence, 25% of figure is colored.

(ii)
We can able to identify that 3 part is shaded out of 5 equal parts.

It is represented by a fraction = \(3\over5\)

= \(3\over5\) × 100

= \(300\over5\)

= 60%

Hence, 60% of figure is colored.

(iii)We can able to identify that 3 part is shaded out of 8 equal parts.

It is represented by a fraction =\( 3\over8\)

= \( 3\over8\) × 100

= \(300\over 8\)

= 37.5%

Hence, 37.5% of figure is colored.

Question 4. Find:
(a) 15% of 250

Solution:-

= \(15\over100\) × 250

= \(15\over2\) × 5

= \(75\over2\)

= 37.5

(b) 1% of 1 hour

Solution:-

1 hour = 60 minutes

1% of 60 minutes

1 minute = 60 seconds

60 minutes = 60 × 60 = 3600 seconds

1% of 3600 seconds

= \(1\over 100\) × 3600

= 1 × 36

= 36 seconds

(c) 20% of ₹ 2500

Solution:-

= \(20\over100\) × 2500

= 20 × 25

= ₹ 500

(d) 75% of 1 kg

Solution:-

1 kg = 1000 g

75% of 1000 g

= \(75\over100\) × 1000

= 75 × 10

= 750 g

So, 30% are children.

Question 5. Find the whole quantity if

(a) 5% of it is 600

Solution:-

Let  the whole quantity be x,

\(5\over100\) × x = 600

x = 600 × \(100\over5\)

x = \(60000\over5\)

x = 12000

(b) 12% of it is Rs 1080.
Solution:-

Let us assume the whole quantity be x,

\(12\over100\) × x = 1080

x = 1080 × \(100\over12\)

x = 540 × \(100\over6\)

x = 90 × 100

x = Rs 9000

(c) 40% of it is 500 km

Solution:-

Let  the whole quantity be x,

\(40\over100\) × x = 500

x = 500 × \(100\over40\)

x = 500 × \(10\over4\)

x = 500 × 2.5

x = 1250 km

(d) 70% of it is 14 minutes

Solution:-

Let  the whole quantity be x,

\(70\over100\) × x = 14

x = 14 × \(100\over70\)

x = 14 × \(10\over7\)

x = 20 minutes

(e) 8% of it is 40 liters

Solution:-

Let the whole quantity be x,

\({8\over100} × x = 40\)

x = 40 × \(100\over8\)

x = 40 × 12.5

x = 500 liters

Question 6. Convert given percent to decimal fractions and also fractions in simplest forms:

(a) 25%

Solution:-

= \(25\over 100\)

= \(1\over4\)

= 0.25

(b) 150%

Solution:-

= \(150\over100\)

= \(3\over2\)

= 1.5

(c) 20%

Solution:-

= \(20\over100\)

=  \(1\over5\)

= 0.2

(d) 5%

Solution:-

= \(5\over100\)

= \(1\over20\)

= 0.05

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

Solution:-

Percentage of female in a city =30%

Percentage of male in a city = 40%

Total percentage of male and female both = 40% + 30% = 70%

Now we have to find the percentage of 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?

Solution:-

Total number of voters in the constituency = 15000

Percentage of people who voted in the election = 60%

Percentage of people who did not voted in the election = 100 – 60= 40%

Total number of voters who did not voted in the election = 40% of 15000

= \({40\over100} × 15000\)

= 0.4 × 15000

= 6000 voters

∴ 6000 voters did not vote.

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

Solution:-

Let us assume Meeta’s salary be ₹ x,

10% of ₹ x = ₹ 4000

\({10\over100} × x = 4000\)

\(x = 4000 × {100\over10}\)

x = 4000 × 10

x = ₹ 40000

∴ Meeta’s salary is ₹ 40000.

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

Solution:-
From the question, it is given that
Total matches played by a local team = 20
Percentage of matches won by the local team = 25%
Then,
Number of matches won by the team = 25% of 20
= \({25\over100} × 20\)
= \(25\over5\)
= 5 matches.
∴The local team won 5 matches out of 20 matches.