Class 8 Maths Chapter 7 Question Answers - Comparing Quantities

Q1: In a computer lab, there are three computers for every six students. How many computers will be needed if there are 24 students?
Ans: From the above question, it is given that,
Then, Number of computers required for six students = is 3
So, the number of computers required for one student = (3/6)= ½
Hence, the Number of computers required for the 24 students = 24 × ½
= 24/2
= 12
Therefore, the Number of computers required for 24 students is 12 computers.

Q2: Convert the given fractional numbers given below to percent.
Ans: 
(i) 1/8
In order to convert a fraction into percentage, multiply it by the fraction of 100 and then put the percent sign %.
= (1/8) × 100 %
= 100/8 %
= 12.5%

(ii) 5/4
In order to convert a fraction into percentage, multiply the fraction by 100 and then put the per cent sign %.
= (5/4) × 100 %
= 500/4 %
= 125%
(iii) 3/40
In order to convert a fraction into percentage, multiply the fraction by 100 and then put the percent sign %.
= (3/40) × 100 %
= 300/40 %
= 30/4 %
= 7.5%

Q3: Find:
(a) 15% of 250
Ans:
We have,
= (15/100) × 250
= (15/10) × 25
= (15/2) × 5
= (75/2)
= 37.5
(b) 1% of 1 hour
We know that 1 hour = 60 minutes
Then,
1% of 60 minutes
1 minute = 60 seconds
60 minutes = 60 × 60 = 3600 seconds
Now,
1% of 3600 seconds
= (1/100) × 3600
= 1 × 36
= 36 seconds
(c) 20% of ₹ 2500
We have,
= (20/100) × 2500
= 20 × 25
= ₹ 500
(d) 75% of 1 kg
We know that 1 kg = 1000 g
Then,75% of 1000 g
= (75/100) × 1000
= 75 × 10
= 750 g

Q4: Convert the given percent to decimal fractions and also convert these fractions in simplest forms:
(i) 25%
Ans:
Firstly convert the given above percentage into a fraction and then convert the fraction into decimal form.
= (25/100)
= ¼
= 0.25
(ii) 150%
Answer:-
Firstly convert the given above percentage into a fraction and then convert the fraction into decimal form.
= (150/100)
= 3/2
= 1.5

Q5: Out of 15,000 voters in a constituency, 60% of people voted. Find the percentage of voters who didn’t vote. Now find out how many of them actually did not vote.
Ans: From the above question, it is given that
Total Number of voters present in the constituency = 15000
The percentage of people that voted in the election is = 60%
The percentage of people who did not vote in the election is = 100 – 60
= 40%
The total number of voters who did not vote in the election is = 40% of 15000
= (40/100) × 15000
= 0.4 × 15000
= 6000 voters
∴ Six thousand voters did not vote.

Q6: Find the ratio of
(a) ₹ 5 to 50 paise
Ans: We know that,
₹ 1 = 100 paise
Then,
₹ 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
We know that,
1 kg = 1000 g
Then,
15 kg = 15 × 1000 = 15000 g
Now we have to find the ratio,
= 15000/210
= 1500/21
= 500/7 … [∵divide both by 3]
So, the required ratio is 500: 7.
(c) 9 m to 27 cm
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.

Q7: It is given that the Population of Rajasthan = is 570 lakhs, and the population of UP = is 1660 lakhs.
The area of Rajasthan is = 3 lakh km sq, and area of UP = 2 lakh km sq.
(a) How many people are present per km sq in both these States?
(b) Which of the above State is less populated?
Ans:
(a) From the above question, it is given that,
The population of the state Rajasthan = 570 lakh
Area of the state Rajasthan = 3 lakh Km2
Then, the final population of the state Rajasthan in 1 km sq area = (570 lakh)/ (3 lakh km2)
= 190 people are there per km2
The population of UP is = 1660 Lakh
Area of UP is = 2 Lakh km2
Then, the population of UP in 1 lakh km sq area = (1660 lakh)/ (2 lakh km2)
= 830 people per km sq
(ii) By comparing the two states, Rajasthan was found to be the less populated state.

Q8: Convert the following given decimal fraction to percent.
(i) 0.65
Ans: Firstly we have to remove the decimal point,
= 65/100
Now,
Multiply it by 100 and then put the percent sign %.
We have,
= (65/100) × 100
= 65%
(ii) 2.1
Firstly we have to remove the decimal point,
= 21/10
Now,
Multiply it by 100 and then put the percent sign %.
We have,
= (21/10) × 100
=210%
(iii) 0.02
Firstly we have to remove the decimal point,
= 2/100Now,
Multiply it by 100 and put the percent sign %.
We have,
= (2/100) × 100
= 2%

Q9: ind the whole quantity if
(i) 5% of it is 600
Ans: 
Let us assume that the whole quantity is x,
Then,
(5/100) × (x) = 600
X = 600 × (100/5)
X = 60000/5
X = 12000
(ii) 12% of it is ₹ 1080.
Let us assume that the whole quantity is x,
Now,
(12/100) × (x) = 1080
X = 1080 × (100/12)
X = 540 × (100/6)
X = 90 × 100
X = ₹ 9000

Q10: In a city, 30% of the public are females, 40% of them are males, and the remaining are children.
What percent of them are children?
Ans:  From the above question, it is given that
Percentage of females in the city =30%
Percentage of males in the city = 40%
Total percentage of both male and female = 40% + 30%
= 70%
Now we will have to find the percentage of children present in the city = 100 – 70
= 30%
So, 30% are children.