Comparing Quantities Ex-8.2

NCERT solutions for Maths Comparing Quantities 

NCERT Solutions for Class 7 Maths Comparing Quantities

Class –VII Mathematics (Ex. 8.2)

Question 1.Convert the given fractional numbers to percent:

(a) $\frac{1}{8}$

(b) $\frac{5}{4}$

(c) $\frac{3}{{40}}$

(d) $\frac{2}{7}$

Answer:

(a) $\frac{1}{8}$ = $\frac{1}{8} \times 100\% = \frac{{25}}{2}\%$ = 12.5%

(b) $\frac{5}{4}$ = $\frac{5}{4} \times 100\% =$ 5 x 25% = 125%

(c) $\frac{3}{{40}}$ = $\frac{3}{{40}} \times 100\% = \frac{3}{2} \times 5\% = \frac{{15}}{2}\%$ = 7.5%

(d) $\frac{2}{7}$ = $\frac{2}{7} \times 100\% = \frac{{200}}{7}\% = 28\frac{4}{7}\%$

NCERT Solutions for Class 7 Maths Exercise 8.2

Question 2.Convert the given decimal fractions to percents:

(a) 0.65

(b) 2.1

(c) 0.02

(d) 12.35

Answer:

(a) 0.65 = $\frac{{65}}{{100}} \times 100\%$ = 65%

(b) 0.02 = $\frac{2}{{100}} \times 100\%$ = 2%

NCERT Solutions for Class 7 Maths Exercise 8.2

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

Answer:

(i) Coloured part = $\frac{1}{4}$

$\therefore$ Percent of coloured part = $\frac{1}{4} \times 100\%$ = 25%

(ii) Coloured part = $\frac{3}{5}$

$\therefore$ Percent of coloured part = $\frac{3}{5} \times 100\%$ = 60%

(iii) Coloured part = $\frac{3}{8}$

$\therefore$ Percent of coloured part = $\frac{3}{8} \times 100\%$ = $\frac{3}{2} \times 25\%$

= 37.5%

Question 4.Find:

(a) 15% of 250

(b) 1% of 1 hour

(c) 20% of Rs. 2500

(d) 75% of 1 kg

Answer:

(a) 15% of 250 = $\frac{{15}}{{100}} \times 250$ = 15 x 2.5 = 37.5

(b) 1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60) seconds

= $\frac{1}{{100}} \times 60 \times 60$ = 6 x 6 = 36 seconds

(c) 20% of Rs. 2500 = $\frac{{20}}{{100}} \times 2500$ = 20 x 25 = Rs. 500

(d) 75% of 1 kg = 75% of 1000 g = $\frac{{75}}{{100}} \times 1000$ = 750 g = 0.750 kg

NCERT Solutions for Class 7 Maths Exercise 8.2

Question 5.Find the whole quantity if:

(a) 5% of it is 600

(b) 12% of it is Rs. 1080

(c) 40% of it is 500 km

(d) 70% of it is 14 minutes

(e) 8% of it is 40 liters

Answer:

Let the whole quantity be $x$ in given questions:

(a) 5% of $x$ = 600 $\Rightarrow$ $\frac{5}{{100}} \times x = 600$

$\Rightarrow$ $x = \frac{{600 \times 100}}{5}$ = 12,000

(b) 12% of $x$ = Rs. 1080 $\Rightarrow$$\frac{{12}}{{100}} \times x = 1080$

$\Rightarrow$ $x = \frac{{1080 \times 100}}{{12}}$ = Rs. 9,000

(c) 40% of $x$ = 500 km $\Rightarrow$ $\frac{{40}}{{100}} \times x = 500$

$\Rightarrow$ $x = \frac{{500 \times 100}}{{40}}$ = 1,250 km

(d) 70% of $x$ = 14 minutes $\Rightarrow$ $\frac{{70}}{{100}} \times x = 14$

$\Rightarrow$ $x = \frac{{14 \times 100}}{{70}}$ = 20 minutes

(e) 8% of $x$ = 40 liters $\Rightarrow$ $\frac{8}{{100}} \times x = 40$

$\Rightarrow$ $x = \frac{{40 \times 100}}{8}$ = 500 liters

NCERT Solutions for Class 7 Maths Exercise 8.2

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

(a) 25%

(b) 150%

(c) 20%

(d) 5%

Answer:

NCERT Solutions for Class 7 Maths Exercise 8.2

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

Answer:

Given: Percentage of females = 30%

Percentage of males = 40%

Total percentage of females and males = 30 + 40 = 70%

Percentage of children = Total percentage – Percentage of males and females

= 100% – 70%

= 30%

Hence, 30% are children.

NCERT Solutions for Class 7 Maths Exercise 8.2

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 voters = 15,000

Percentage of voted candidates = 60%

Percentage of not voted candidates = 100 – 60 = 40%

Actual candidates, who did not vote = 40% of 15000

= $\frac{{40}}{{100}} \times 15000$ = 6,000

Hence, 6,000 candidates did not vote.

NCERT Solutions for Class 7 Maths Exercise 8.2

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

Answer:

Let Meera’s salary be Rs.$x.$

Now, 10% of salary = Rs. 400

$\Rightarrow$ 10% of $x$ = Rs. 400

$\Rightarrow$ $\frac{{10}}{{100}} \times x = 400$

$\Rightarrow$ $x = \frac{{400 \times 100}}{{10}}$

$\Rightarrow$ $x =$ 4,000

Hence, Meera’s salary is Rs. 4,000.

NCERT Solutions for Class 7 Maths Exercise 8.2

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 played by cricket team = 20

Percentage of won matches = 25%

Total matches won by them = 25% of 20

= $\frac{{25}}{{100}} \times 20$

= 5

Hence, they won 5 matches.