These NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.1
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
Answer:
(a) ₹ 5 = 5 x 100 paise
0 = 500 paise
₹ 5 : 50 paise = 500 paise : 50 paise
= 500 : 50
= 10 : 1
(b) 15 kg = 15×1000 g
= 15000g
15 kg to 210 g = 15000: 210 g
= 1500 : 21
= 500 : 7
(c) 9 m = 9 x 100 cm
= 900 cm
9 m : 27 cm= 900 : 27
= 100:3 (÷9)
(d) 30 days = 30 x 24 hours
= 720 hours
30 days : 36 hours = 720 : 36
= 20:1 (÷36)
Question 2.
In a computer lab there are 3 computers for every6 students. How many computers will be needed for 24 students?
Ans: Let x be the required number of computers.
3 : x = 6:24
\(\frac{3}{x}=\frac{6}{24}\)
6x = 3 x 24
x = \(\frac{3 \times 24}{6}\) = 3 x 4 = 12
Hence, 12 computers will be needed for 24 students.
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?
Answer:
(i) Population of Rajasthan
= 570 lakhs
Area of Rajasthan
= 3 lakhs km2
Population per km2
= \(\frac{570}{3}\) lakhs km2
= 190 lakhs per km2
In Rajasthan, there are 190 lakh people per km2
For UP
population = 1660 lakhs
Area = 2 lakhs per km2
population per km2
= \(\frac{1660}{2}\) per km2
= 830 lakhs per km2
In UP, there are 830 lakhs people per km2
(ii) 190 lakhs < 830 lakhs
∴ Rajasthan is less populated state.