Short Question Answer: Comparing Quantities
Q1. In a class of 45 students 40% are girls. Find the no. of boys.
Ans: Given: Girls percentage in class= 40%
Total no. of students =45
No. of girls = 45 × 40 / 100 = 45 × 2 / 5 = 18
No. of boys = Total no. of students - No. of girls
= 45 - 18
= 27
Q2. Find the ratio of
(a) 18m to 45cm
Ans: Let's convert both lengths into the same unit.
1m = 100cm
∴18m = 18 x 100cm
18m to 45cm = 1800 / 45
= 40 / 1
= 40 : 1
(b) 20 days to 48 hours
Ans: First convert both time into same units
1 day = 24 hours
20 days = 20 × 24 = 480 hours
20 days : 48 hours = 480 : 48
= 480 / 48 = 10
Required Ratio is 10 : 1
Q3. In a city, 35% of population are males and 25% are females and the remaining are children. What is the percentage of children in the city?
Ans: The total percentage = 100% of males = 35%
% of females = 25%
Also, Total % = % of (Females + males + children)
∴ % of children = Total % - % of females - % of males
= (100 - 35 - 25)%
= (100 - 60)%
= 40%
Q4. Find:
(a) 80% of 2kg's
(b) 25% of 3000
Ans:
(a) 80% of 2kg's
We know, 2kg = 2000g
80% of 2000g = 80% × 2000g
= 80 / 100 × 2000g
= 80 × 20g = 1600g = 1.6kg
(b) 25% of 3000
25 / 100 × 3000
= 25 × 30
= 750
Q5. Convert given percent to decimal fractions and also to fractions in simplest form
(a) 10%
(b) 40%
Ans: To convert percent into decimal fraction we will divide the number by 100
(a) 10%
= 10 / 100
= 1 / 10
= 0.1
(b) 40%
= 40 / 100
= 4 / 10
= 0.4
Q6. Mithali buys a TV at 12,000 and sells it at a profit of 20%. How much money does she get?
Ans: Mithali buys TV = Cost price of TV = 12,000
Mithali sells TV at profit = 20% of 12000
= 20 / 100 × 12,000 = 20 × 120 = Rs.2400
Now, Selling price = cost price + profit
= 12,000 + 2,400 = Rs. 14,400
Therefore, Mithali get Rs. 14,400
Q7. Find
(a) 
(b) 30% of 150Ans:
(a) 
We know, 
(b) 30% of 150
= 30 / 100 × 150
= 3 × 15 = 45
Q8. Find the whole quantity if
(a) 10% of it is 800
(b) 15% of it is 1050
Ans:
(a) 10% of it is 800
Let quantity is x
∴10% of x = 800
⇒ 10% × x = 800
⇒ 10100 × x = 800
⇒ 110 × x = 800
⇒x = 800 × 10
∴ x = 8000
So, whole quantity = 8000
(b) 15% of it is 1050
Let the quantity is x
∴15% of x = 1050
⇒15% × x = 1050
⇒ 15100 × x = 1050
⇒ 320 × x = 1050
⇒ x = 1050 × 203
∴ x = 350 × 20
⇒ x = 7000
Q9. Manvita saves Rs. 9000 from her salary every month. If it is 5% of her salary. Find her salary.
Ans: Let Manvita's salary = xRs.
5% of Manvita's Salary = Rs. 9000
∴5% of x = 9000
⇒ 5 / 100 × x = 9000
⇒ x = 9000 × 100 / 5
⇒ x = 1800 × 100
∴ x = 1,80,000
Therefore, Manvita's salary is 1,80,000
Q10. convert the following fractions to percent.
(a) 34
(b) 25
Ans:
(a) We'll multiply the numerator and denominator by 25 to make the denominator 100.
3 / 4 × 25 / 25 = 75 / 100 = 75%
(b) We'll multiply the numerator and denominator by 20 to make the denominator 100.
2 / 5 × 20 / 20 = 40 / 100 = 40%
Q11. Convert the following into percent
(a) 34 / 50
(b) 1 / 4
(c) 0.03
Ans: First, we will make denominator 100, and then we will convert that number into percent
(a) 34 / 50 × 22 = 68 / 100 = 68%
(b) 1 / 4 × 2525 = 25 / 100 = 25%
(c) 0.03 = 3 / 100 = 3%
Q12. Out of 24,000voters in a constituency 48% voted. Find the no. of voters who did not vote.
Ans: Total voters = 24,000
Vote percentage = 48%
No. of Voters voted = 48% of 12,000
= 48 / 100 × 24,000=48 × 240 = 11,520
No. of voters did not vote = Total voters - No. of voters voted
= 24,000 - 11,520 = 12,480
Therefore, 12,480 people did not vote.
Q13. What rate gives an interest of Rs. 540on a sum of Rs. 18000in 3 years?
Ans: Given, Interest, I = Rs. 540
Principal,P = Rs. 18000
Time, T = 3 years
We know, Interest = Principal × Rate × Time / 100
∴ Rate = Interest × 100 / Principal × Time
= 540 × 100 / 18000 × 3
= 180 / 180
= 1%
