Comparing Quantities - Solutions

 CBSE Class –VII Mathematics

NCERT Solutions
Chapter 8 Comparing Quantities (Ex. 8.1)

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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

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

⇒$\Rightarrow$ 500 paise to 50 paise

Thus, the ratio is = 50050=101$\frac{500}{50}=\frac{10}{1}$ = 10 : 1

(b) 15 kg to 210 g

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

⇒$\Rightarrow$ 15000 g to 210 g

Thus, the ratio is = 15000210=5007$\frac{15000}{210}=\frac{500}{7}$ = 500 : 7

(c) 9 m to 27 cm

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

⇒$\Rightarrow$ 900 cm to 27 cm

Thus, the ratio is = 90027=1003$\frac{900}{27}=\frac{100}{3}$ = 100 :3

(d) 30 days to 36 hours

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

⇒$\Rightarrow$ 720 hours to 36 hours

Thus, the ratio is = 72036=201$\frac{720}{36}=\frac{20}{1}$ = 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 = 36$\frac{3}{6}$ computers
24 students needs = 36$\frac{3}{6}$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 km2$k{m}^2$and area of U.P. = 2 lakh km2$k{m}^2$.

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

(ii) Which state is less populated?

Answer: (i) People present per km2$k{m}^2$= PopulationArea$\frac{\text{Population}}{\text{Area}}$

In Rajasthan = 570 lakhs3 lakhs km2$\frac{570\text{ lakhs}}{\text{3 lakhs k}{\text{m}}^2}$ = 190 people per km2$k{m}^2$

In U.P. = 1660 lakhs2 lakh km2$\frac{\text{1660 lakhs}}{\text{2 lakh k}{\text{m}}^2}$ = 830 people per km2$k{m}^2$

(ii) Rajasthan is less populated.