These NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.1

Question 1.

Find the ratio of

(a) ₹ 5 to 50 paise

(b) 15 kg to 210 g

(c) 9 m to 27 cm

(d) 30 days to 36 hours

Answer:

(a) ₹ 5 = 5 x 100 paise

0 = 500 paise

₹ 5 : 50 paise = 500 paise : 50 paise

= 500 : 50

= 10 : 1

(b) 15 kg = 15×1000 g

= 15000g

15 kg to 210 g = 15000: 210 g

= 1500 : 21

= 500 : 7

(c) 9 m = 9 x 100 cm

= 900 cm

9 m : 27 cm= 900 : 27

= 100:3 (÷9)

(d) 30 days = 30 x 24 hours

= 720 hours

30 days : 36 hours = 720 : 36

= 20:1 (÷36)

Question 2.

In a computer lab there are 3 computers for every6 students. How many computers will be needed for 24 students?

Ans: Let x be the required number of computers.

3 : x = 6:24

\(\frac{3}{x}=\frac{6}{24}\)

6x = 3 x 24

x = \(\frac{3 \times 24}{6}\) = 3 x 4 = 12

Hence, 12 computers will be needed for 24 students.

Question 3.

Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs. Area of Rajasthan = 3 lakh km2 and area of UP = 2 lakh km^{2}.

(i) How many people are there per km2 in both these states?

(ii) Which state is less populated?

Answer:

(i) Population of Rajasthan

= 570 lakhs

Area of Rajasthan

= 3 lakhs km^{2}

Population per km^{2}

= \(\frac{570}{3}\) lakhs km^{2}

= 190 lakhs per km^{2}

In Rajasthan, there are 190 lakh people per km^{2}

For UP

population = 1660 lakhs

Area = 2 lakhs per km^{2}

population per km^{2}

= \(\frac{1660}{2}\) per km^{2}

= 830 lakhs per km^{2}

In UP, there are 830 lakhs people per km^{2}

(ii) 190 lakhs < 830 lakhs

∴ Rajasthan is less populated state.