Ratio and Proportion Questions & Answers

Question 26

Medium

4 years ago, the ratio of the ages of P and Q was 11 : 4. The ratio of their present ages is 15 : 8. What is the sum of their present ages?

A 23 years

B 15 years

C 27 years

D 31 years

Correct Answer: A

Explanation:

Step 1: Let the present ages be 15k and 8k. Step 2: 4 years ago: (15k − 4) : (8k − 4) = 11 : 4 → 4(15k − 4) = 11(8k − 4). Step 3: 28k = 28 → k = 1; ages are 15 and 8 years, so sum = 23 years.

Question 27

Hard

A vessel contains 98 litres of a mixture of milk and water in the ratio 4 : 3. How many litres of the mixture must be taken out and replaced with water so that the ratio becomes 24 : 25?

A 28 litres

B 12 litres

C 7 litres

D 14 litres

Correct Answer: D

Explanation:

Step 1: Milk = 98 × 4/7 = 56 L. Step 2: The total stays 98 L, so in the final ratio 24 : 25 milk must be 98 × 24/49 = 48 L. Step 3: Removing x L of mixture leaves milk 56 × (98 − x)/98 = 48 → 98 − x = 84 → x = 14 litres.

Question 28

Easy

If a : b = 9 : 5, find (3a + b) : (3a − b).

A 1 : 1

B 16 : 11

C 11 : 16

D 17 : 11

Correct Answer: B

Explanation:

Step 1: Since a : b = 9 : 5, let a = 9k and b = 5k. Step 2: 3a + b = 27k + 5k = 32k and 3a − b = 27k − 5k = 22k. Step 3: Ratio = 32k : 22k = 32 : 22 = 16 : 11.

Question 29

Medium

Two vessels contain milk and water in the ratios 4 : 7 and 4 : 1. If the contents of the two vessels are mixed in equal quantities, what is the ratio of milk to water in the new mixture?

A 1 : 1

B 23 : 32

C 33 : 23

D 32 : 23

Correct Answer: D

Explanation:

Step 1: Milk is 4/11 of vessel 1 and 4/5 of vessel 2. Step 2: Take 1 unit of vessel 1 and 1 unit of vessel 2: milk = 1 × 4/11 + 1 × 4/5 = 64/55. Step 3: Water = 2 − 64/55 = 46/55, so milk : water = 64/55 : 46/55 = 32 : 23.

Question 30

Medium

If x : y = 8 : 7, find (x² + y²) : (x² − y²).

A 15 : 1

B 64 : 49

C 113 : 15

D 15 : 113

Correct Answer: C

Explanation:

Step 1: Let x = 8k and y = 7k. Step 2: x² + y² = (64 + 49)k² = 113k² and x² − y² = (64 − 49)k² = 15k². Step 3: Ratio = 113 : 15.

Ratio and Proportion Practice Questions