Ratio and Proportion Questions & Answers

Question 11

Easy

Find the fourth proportional to 4, 20 and 53.

A 10.6

B 1.51

C 265

D 267

Correct Answer: C

Explanation:

Step 1: Let the fourth proportional be x, so 4 : 20 :: 53 : x. Step 2: Product of extremes = product of means: 4 × x = 20 × 53 = 1060. Step 3: x = 1060 ÷ 4 = 265.

Question 12

Medium

An alloy of 50 kg contains gold and copper in the ratio 3 : 2. How much gold must be added to make the ratio 7 : 4?

A 15 kg

B 5 kg

C 4 kg

D 35 kg

Correct Answer: B

Explanation:

Step 1: Gold = 50 × 3/5 = 30 kg and copper = 20 kg. Step 2: Adding gold does not change the copper, so (30 + x) : 20 = 7 : 4. Step 3: 30 + x = 20 × 7/4 = 35 → x = 5 kg.

Question 13

Medium

Divide ₹1650 among A, B and C such that 8 times A's share = 2 times B's share = 5 times C's share. What is A's share?

A ₹400

B ₹250

C ₹1000

D ₹300

Correct Answer: B

Explanation:

Step 1: Let 8A = 2B = 5C = k, so A : B : C = 1/8 : 1/2 : 1/5. Step 2: Multiply by the LCM 40: A : B : C = 5 : 20 : 8. Step 3: 1 part = 1650 ÷ 33 = 50, so A = 5 × 50 = ₹250.

Question 14

Medium

In a school, the ratio of boys to girls is 5 : 4. If 21 more girls join, the ratio becomes 10 : 11. How many boys were there originally?

A 70

B 56

C 91

D 73

Correct Answer: A

Explanation:

Step 1: Let boys = 5k and girls = 4k. Step 2: After 21 girls join: 5k : (4k + 21) = 10 : 11. Step 3: 15k = 210 → k = 14, so boys originally = 5 × 14 = 70.

Question 15

Medium

x varies inversely as the square of y. If x = 20 when y = 3, find x when y = 2.

A 45

B 30

C 8.89

D 46

Correct Answer: A

Explanation:

Step 1: x ∝ 1/y² means xy² = k. Step 2: Using x = 20, y = 3: k = 20 × 3² = 20 × 9 = 180. Step 3: When y = 2: x = 180 ÷ 2² = 180 ÷ 4 = 45.

Ratio and Proportion Practice Questions