# NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities

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

Ex 8.1 Class 7 Maths 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

Solution:

(a) ₹ 5 to 50 paise

Converting the given quantities into same units, we have

₹ 5 = 5 × 100 = 500 paise

∴ ₹ 5 : 50 paise

= 500 paise : 50 paise [∵ ₹ 1 = 100 paise]

= 10 : 1

So, required ratio is 10 : 1.

(b) 15 kg to 210 g

Converting the given quantities into same units, we have

15 kg = 15 × 1000

= 15000 g [∵ 1 kg = 1000 g]

∴ 15 kg : 210 g = 15000 g : 210 g

= 1500 : 21

= 500 : 7

So, the required ratio is 500 : 7.

(c) 9 m to 27 cm

Converting the given quantities into same units, we have

9 m = 9 × 100 = 900 cm

∴ 9m: 27 cm = 900 cm : 27 cm [∵ 1 m = 100 cm]

= 100 : 3

So, the required ratio is 100 : 3.

(d) 30 days to 36 hours

Converting the given quantities into same

units, we have

30 days = 30 × 24 hours [ ∵ 1 day = 24 hours]

= 720 hours

∴ 30 days : 36 hours

= 720 hours : 36 hours = 20:1

So, the required ratio is 20 : 1.

Ex 8.1 Class 7 Maths Question 2.

In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

Solution:

Using Unitary Method, we have

6 students require 3 computers

∴ 1 student will require = \(\frac{3}{6}\) computers

∴ 24 students will require = \(\frac{3}{6}\) x 24 computers

= 3 × 4 computers = 12 computers

Hence the number of computers required = 12.

Ex 8.1 Class 7 Maths 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 km2.

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

(ii) Which State is less populated?

Solution:

Given:

Population of Rajasthan = 570 lakhs

Population of UP = 1660 lakhs

Area of Rajasthan = 3 lakh km^{2}

Area of UP = 2 lakh km^{2}

(i) Number of people per km^{2} of Rajasthan 5

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

= 190 per km^{2}

Number of people in UP = 1660 lakhs

Area of UP = 2 lakh km^{2}

Number of people per km^{2} of UP

= \(=\frac{1660 \text { lakhs }}{2 \text { lakh } \mathrm{km}^{2}}=830 \text { per } \mathrm{km}^{2}\)

Since 190 per km^{2}< 830 per km^{2}

(ii) Rajasthan is less populated state.