Comparing Quantities Ex-8.1

NCERT solutions for Maths Comparing Quantities

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

$\Rightarrow$ 5 x 100 paise to 50 paise

[$\because$Rs. 1 = 100 paise]

$\Rightarrow$ 500 paise to 50 paise

Thus, the ratio is = $\frac{{500}}{{50}} = \frac{{10}}{1}$ = 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 = $\frac{{15000}}{{210}} = \frac{{500}}{7}$ = 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 = $\frac{{900}}{{27}} = \frac{{100}}{3}$ = 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 = $\frac{{720}}{{36}} = \frac{{20}}{1}$ = 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 = $\frac{{65}}{{100}} \times 100\%$ = 65%

(b) 0.02 = $\frac{2}{{100}} \times 100\%$ = 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 $k{m^2}$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 = $\frac{{570{\text{ lakhs}}}}{{{\text{3 lakhs per k}}{{\text{m}}^2}}}$ = 190 people $k{m^2}$

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

(ii) Rajasthan is less populated.

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