Class 8 Maths Chapter 7 HOTS Questions - Comparing Quantities

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Q1: Express 25% and 12% as decimals.
Ans: 25% = 25/100 = 0.25
12% = 12/100 = 0.12

Q2: Express 45% and 78% as a fraction.
Ans: 45% = 45/100 = 9/20
78% = 78/100 = 39/50

Q3: Calculate the ratio of 5 m to 20 km.
Ans: 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

Q4: 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?
Ans: 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.

Q5: If 72% of 25 students like maths, find out the number of students who do not like mathematics?
Ans: 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

Q6: 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.
Ans: 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.

Q7: 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.
Ans: 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.

Q8: In a certain school, there are 456 girls. Calculate the total number of students if 24% of the total students are boys.
Ans: 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.