Class 8 Maths Chapter 7 Practice Question Answers - Comparing Quantities

Q1: In a certain school, there are 456 girls. Calculate the total number of students if 24% of the total students are boys.
Sol: Assume the total number of students to be 100.
It is given that 24% are boys.
So, total number of boys = 24% of 100 = 24
Thus, the total number of girls will be = (100-24)% i.e. 76%.
So, the total number of girls = 76% of 100 = 76
But, it is given that there are 456 girls.
Now, for 76 girls, total students are 100
For, 1 girl, total students will be 100/76
Therefore, for 456 girls, the total number of students will be = 100/76 × 456 = 45600/76 = 600
Thus, the total number of students = 600.

Q2: A person goes shopping and spends 75% of his money. If he is now left with Rs. 600, find out how much he had in the beginning.
Sol:
Let “x” be the initial amount that he had in the beginning.
As per the given question, the person spent 75% of Rs.x and is left with Rs. 600.
So, the amount he spent = x – 600
⇒ 75% of x = x – 600
⇒ (75/100) × x = x – 600
⇒ 75x = 100x – 60,000
⇒ 25x = 60,000
Or, x = 2400.
Thus, the person had Rs. 2400 initially.

Q3: A student got 150 marks out of 200 in maths and got 120 marks out of 180 in science. In which subject did the student perform better?
Sol:
Express the marks in the form of ratios.
For maths, ratio = 150/200 = ¾
For science, ratio = 120/180= ⅔
Here, the ratio ¾ shows 75% (¾ × 100 = 75) and the ratio ⅔ shows 66.6% (⅔ × 100 = 66.6).
Thus, the student performed better in the maths exam.

Q4: Express 45% and 78% as a fraction.
Sol:
45% = 45/100 = 9/20
78% = 78/100 = 39/50

Q5: Express 25% and 12% as decimals.
Sol:
25% = 25/100 = 0.25
12% = 12/100 = 0.12

Q6: Calculate the ratio of 5 m to 20 km.
Sol:
First, make both the units the same.
So, we need to convert 20 km to the equivalent meter, i.e. “m”.
⇒ 20km = (20 × 1000)m
Thus, the ratio of 5 m to 20 km = 5/20000
= 1:4000

Q7: If 72% of 25 students like maths, find out the number of students who do not like mathematics?
Sol:
Given, 72% of 25 students like maths.
Hence, 72% of 25 = (72/100) × 25 = 18 students
Now, from 25 students, 18 students like maths
Thus, the number of students who do not like maths = 25 – 18 = 7 students

Q8: A shopkeeper bought two phones for Rs. 8,000 each. After selling the phones, there was a loss of 4% on the 1st phone while a profit of 8% on the 2nd phone. Calculate the overall gain or loss per cent on the whole transaction.
Sol: As the shopkeeper bought both phones at Rs. 8000 each.
Total cost price = Rs. 16,000
Assume that the cost price of the 1st phone is Rs. 100
Consider the deal of phone 1,
As it is given, there is 4% loss, the selling price will be = Rs. 96
For CP = 100, SP = 96
So, for CP = 1, SP = 96/100
Now, given, CP = 8000
Hence, SP = 96/100 × 8000 = 7680
Thus, the selling price of 1st phone = Rs. 7680
Consider the deal of phone 2, there is an 8% profit.
Hence, the selling price will be = Rs. 108
For CP = 100, SP = 108
So, for CP = 1, SP = 108/100
Now, given CP = 8000
hence, SP = 108/100 × 8000 = 8640
Thus, the selling price of 2nd phone = Rs. 8640
Here, the total selling price will be = Rs. 7680 + Rs. 8640 = 16320
Now, it can be seen that,
Total selling price > total cost price i.e. Rs. 16320 > Rs. 16000
So, there is a profit of Rs. (16320 – 16000) = Rs. 320
Now, the overall profit percentage will be-
Profit% = (Profit/Total Cost Price) × 100 = (320/16000) × 100 = 2
Therefore, there is a total of 2% profit for the whole transaction.

Q9: Apala has Rs 200 with her, and she spent 80% from the amount she had. Calculate the money left with her.
(a)Rs 20
(b) Rs 10
(c) Rs 40
(d) Rs 30
Ans: (c)
Sol: Apala had Rs 200, and she spent 80% of it.
Amount spent = 80% of Rs 200 = 0.8 x Rs 200 = Rs 160
Money left with her = Total amount - Amount spent = Rs. 200 - Rs. 160 = Rs. 40
So, the correct answer is: (c) Rs. 40

Q10: Meenu bought a fridge for Rs 10000 and then sold it for Rs 8000. Calculate her loss.
(a) Rs 12000
(b) Rs 8000
(c) Rs 2000
(d) Rs 10000
Ans: (c)
Sol: Meenu bought a fridge for Rs 10000 and sold it for Rs 8000.
Loss = Cost Price - Selling Price
Loss = Rs 10000 - Rs 8000
Loss = Rs 2000
So, the correct answer is: (c) Rs 2000

Q11: What is the ratio of 10 m to 1 km?
(a) 10 : 1
(b) 1 : 10
(c) 100 : 1
(d) 1 : 100
Ans: (d)
Sol: 
1 kilometer (km) is equal to 1000 meters (m). Therefore, the ratio of 10 m to 1 km can be calculated as:
10 m : 1000 m
Simplifying this ratio by dividing both sides by 10:
1 m : 100 m
Further simplifying by dividing both sides by 100:
1 : 100
So, the correct answer is: (d) 1 : 100

Q12: What is the ratio 1 : 4 converted to percentage?
(a) 50%
(b) 20%
(c) 75%
(d) 4%
Ans: (b)
Sol: To convert a ratio to a percentage, you need to divide the first term of the ratio by the sum of both terms, and then multiply by 100.
Given ratio: 1 : 4
Percentage = (1 / (1 + 4)) x 100 = (1/5) x 100 = 20%
So, the correct answer is:
The ratio 1 : 4 converted to a percentage is 20%.