Ratio and Proportion Questions & Answers

Question 6

Easy

The angles of a triangle are in the ratio 6 : 7 : 5. What is the smallest angle?

A 60°

B 52°

C 50°

D 48°

Correct Answer: C

Explanation:

Step 1: The angles of a triangle add up to 180°. Step 2: Total parts = 6 + 7 + 5 = 18, so 1 part = 180° ÷ 18 = 10°. Step 3: The angles are 60°, 70° and 50°, so the smallest angle = 50°.

Question 7

Easy

The length and breadth of a rectangle are in the ratio 7 : 3. If its perimeter is 100 m, what is its area?

A 105 m²

B 250 m²

C 525 m²

D 550 m²

Correct Answer: C

Explanation:

Step 1: Let length = 7k and breadth = 3k. Step 2: Perimeter = 2(7k + 3k) = 20k = 100, so k = 5. Step 3: Length = 35 m, breadth = 15 m, so area = 35 × 15 = 525 m².

Question 8

Medium

A bag contains ₹1, 50-paise and 25-paise coins in the ratio 1 : 3 : 8. If the total amount is ₹72, how many ₹1 coins are there?

A 48 coins

B 192 coins

C 16 coins

D 32 coins

Correct Answer: C

Explanation:

Step 1: Let the numbers of coins be k, 3k and 8k. Step 2: Their values are ₹1k, ₹1.5k and ₹2k, so total = ₹4.5k = ₹72 → k = 16. Step 3: ₹1 coins = 1 × 16 = 16.

Question 9

Easy

Find the mean proportional between 216 and 294.

A 255

B 258

C 504

D 252

Correct Answer: D

Explanation:

Step 1: Let the mean proportional be x, so 216 : x :: x : 294. Step 2: Then x² = 216 × 294 = 63504. Step 3: x = √63504 = 252.

Question 10

Medium

What number must be added to each term of the ratio 11 : 21 to make it 12 : 17?

A 14

B 12

C 13

D 15

Correct Answer: C

Explanation:

Step 1: Let x be added: (11 + x) : (21 + x) = 12 : 17. Step 2: Cross-multiply: 17(11 + x) = 12(21 + x) → 187 + 17x = 252 + 12x. Step 3: 5x = 65 → x = 13. Check: 24 : 34 = 12 : 17.

Ratio and Proportion Practice Questions