### Comparing Quantities - Solutions

CBSE Class –VII Mathematics

NCERT Solutions
Chapter 8 Comparing Quantities (Ex. 8.1)

Question 1. Find the ratio of:

(a) Rs. 5 to 50 paise

(b) 15 kg to 210 g

(c) 9 m to 27 cm

(d) 30 days to 36 hours

Answer: To find ratios, both quantities should be in same unit.

(a) Rs. 5 to 50 paise

$⇒$ 5 x 100 paise to 50 paise            [$\because$Rs. 1 = 100 paise]

$⇒$ 500 paise to 50 paise

Thus, the ratio is = $\frac{500}{50}=\frac{10}{1}$ = 10 : 1

(b) 15 kg to 210 g

$⇒$ 15 x 1000 g to 210 g                   [ $\because$ 1 kg = 1000 g]

$⇒$ 15000 g to 210 g

Thus, the ratio is = $\frac{15000}{210}=\frac{500}{7}$ = 500 : 7

(c) 9 m to 27 cm

$⇒$ 9 x 100 cm to 27 cm                   [ $\because$ 1 m = 100 cm]

$⇒$ 900 cm to 27 cm

Thus, the ratio is = $\frac{900}{27}=\frac{100}{3}$ = 100 :3

(d) 30 days to 36 hours

$⇒$ 30 x 24 hours to 36 hours           [ $\because$ 1 day = 24 hours]

$⇒$ 720 hours to 36 hours

Thus, the ratio is = $\frac{720}{36}=\frac{20}{1}$ = 20 : 1

Question 2. In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

Answer: 6 students needed = 3 computers
Therefore 1 student needs = $\frac{3}{6}$ computers
24 students needs = $\frac{3}{6}$times 24 = 12 computers
Thus, 12 computers will be needed for 24 students.

Question 3. Population of Rajasthan = 570 lakhs and population of U.P. = 1660 lakhs. Area of Rajasthan = 3 lakh $k{m}^{2}$and area of U.P. = 2 lakh $k{m}^{2}$.

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

(ii) Which state is less populated?

Answer: (i) People present per $k{m}^{2}$$\frac{\text{Population}}{\text{Area}}$

In Rajasthan =  = 190 people per $k{m}^{2}$

In U.P. = $\frac{\text{1660 lakhs}}{\text{2 lakh k}{\text{m}}^{2}}$ = 830 people per $k{m}^{2}$

(ii) Rajasthan is less populated.