Percentage, Ratio and Proportion — Practice

Question 1

Express 3/5 as a percentage.
(a) 60% (b) 35% (c) 53% (d) 65%

Accepted Answer

(a) 60%.

A fraction becomes a percentage when multiplied by 100: (3/5) × 100 = 60%.

Question 2

Find 15% of 240.
(a) 36 (b) 24 (c) 40 (d) 32

Accepted Answer

(a) 36.

Part = (rate/100) × whole = (15/100) × 240 = 36.

Question 3

Divide ₹5,000 between two people in the ratio 3 : 2. What is the larger share?
(a) ₹3,000 (b) ₹2,500 (c) ₹2,000 (d) ₹3,500

Accepted Answer

(a) ₹3,000.

Total parts = 3 + 2 = 5. Larger share = (3/5) × 5,000 = ₹3,000 (the other person gets ₹2,000).

Question 4

A number, when increased by 25%, becomes 250. What was the original number?
(a) 200 (b) 187.5 (c) 225 (d) 210

Accepted Answer

(a) 200.

Original × 1.25 = 250, so original = 250 ÷ 1.25 = 200. Subtracting 25% from 250 would be wrong — you must divide by the factor 1.25.

Question 5

A quantity falls from 500 to 400. By what percentage did it decrease?
(a) 20% (b) 25% (c) 15% (d) 10%

Accepted Answer

(a) 20%.

Decrease = 500 − 400 = 100. Percentage decrease = (100/500) × 100 = 20%. (Note a rise from 400 to 500 would be 25%, since the base differs.)

Question 6

If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c.
(a) 8 : 12 : 15 (b) 2 : 3 : 5 (c) 8 : 12 : 20 (d) 6 : 12 : 15

Accepted Answer

(a) 8 : 12 : 15.

Make b common. a : b = 2 : 3 = 8 : 12; b : c = 4 : 5 = 12 : 15. So a : b : c = 8 : 12 : 15.

Question 7

The price of an article is increased by 10% and then by a further 20%. What is the net percentage increase?
(a) 32% (b) 30% (c) 33% (d) 28%

Accepted Answer

(a) 32%.

Net factor = 1.10 × 1.20 = 1.32, a 32% increase. Successive changes multiply, so you cannot simply add 10% and 20% to get 30%.

Question 8

If 6 workers can finish a job in 10 days, how many days will 4 workers take, working at the same rate?
(a) 15 days (b) 12 days (c) 20 days (d) 8 days

Accepted Answer

(a) 15 days.

The work is 6 × 10 = 60 worker-days. With 4 workers, time = 60 ÷ 4 = 15 days. Fewer workers take more days — an inverse proportion (x₁y₁ = x₂y₂).

Practice — Percentage, Ratio and Proportion