Class 7 Comparing Quantities Ex 8.1

Question 1. Find the ratio of:
(a) Rs 5 to 50 paise

Solution:-
We know that,
Rs 1 = 100 paise
Then,
Rs 5 = 5 × 100 = 500 paise
Now we have to find the ratio,
= ⁵⁰⁰/₅₀
= ¹⁰/₁
So, the required ratio is 10: 1.

(b) 15 kg to 210 g
Solution:-
We know that,
1 kg = 1000 g
Then,
15 kg = 15 × 1000 = 15000 g
Now we have to find the ratio,
= ¹⁵⁰⁰⁰/₂₁₀
= ⁵⁰⁰/₇
So, the required ratio is 500: 7.

(c) 9 m to 27 cm
Solution:-
We know that,
1 m = 100 cm
Then,
9 m = 9 × 100 = 900 cm
Now we have to find the ratio,
= ⁹⁰⁰/₂₇
= ¹⁰⁰/₃ … [∵divide both by 9]
So, the required ratio is 100: 3.

(d) 30 days to 36 hours
Solution:-
We know that,
1 day = 24 hours
Then,
30 days = 30 × 24 = 720 hours
Now we have to find the ratio,
= ⁷²⁰/₃₆
= ²⁰/₁ … [∵divide both by 36]
So, the required ratio is 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?

Solution:-
From the question it is given that,
Number of computer required for 6 students = 3
So, number of computer required for 1 student = (3/6)
= ½
So, number of computer required for 24 students = 24 × ½
= ²⁴/₂
= 12
∴Number of computer required for 24 students is 12 computers.

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?

Solution:-
(i) From the question, it is given that,
Population of Rajasthan = 570 lakh
Area of Rajasthan = 3 lakh km²
Then, population of Rajasthan in 1 km² area = (570 lakh)/ (3 lakh km²)= 190 people per km²
Population of UP = 1660 Lakh
Area of UP = 2 Lakh km²
Then, population of UP in 1 lakh km² area = (1660 lakh)/ (2 lakh km²)
= 830 people per km²

(ii) By comparing the two states Rajasthan is the less populated state.