NCERT Solutions for Class 7 Maths Exercise 8.1

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NCERT solutions for Maths Comparing Quantities Download as PDF

NCERT Solutions for Class 7 Maths Comparing Quantities

Class –VII Mathematics (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

{tex} \Rightarrow {/tex} 5 x 100 paise to 50 paise

[{tex}\because {/tex}Rs. 1 = 100 paise]

{tex} \Rightarrow {/tex} 500 paise to 50 paise

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

(b) 15 kg to 210 g

{tex} \Rightarrow {/tex} 15 x 1000 g to 210 g [ {tex}\because {/tex} 1 kg = 1000 g]

{tex} \Rightarrow {/tex} 15000 g to 210 g

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

(c) 9 m to 27 cm

{tex} \Rightarrow {/tex} 9 x 100 cm to 27 cm [ {tex}\because {/tex} 1 m = 100 cm]

{tex} \Rightarrow {/tex} 900 cm to 27 cm

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

(d) 30 days to 36 hours

{tex} \Rightarrow {/tex} 30 x 24 hours to 36 hours [ {tex}\because {/tex} 1 day = 24 hours]

{tex} \Rightarrow {/tex} 720 hours to 36 hours

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

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NCERT Solutions for Class 7 Maths Exercise 8.1

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

Answer:

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

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

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NCERT Solutions for Class 7 Maths Exercise 8.1

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

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

(ii) Which state is less populated?

Answer:

(i) People present per {tex}k{m^2}{/tex}= {tex}\frac{{{\text{Population}}}}{{{\text{Area}}}}{/tex}

In Rajasthan = {tex}\frac{{570{\text{ lakhs}}}}{{{\text{3 lakhs per k}}{{\text{m}}^2}}}{/tex} = 190 people {tex}k{m^2}{/tex}

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

(ii) Rajasthan is less populated.

NCERT Solutions for Class 7 Maths Exercise 8.1

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