The ratio between two numbers is 2 : 11. If the difference between the numbers is 81, find the smaller number.

Question

The ratio between two numbers is 2 : 11. If the difference between the numbers is 81, find the smaller number.

1. A. 19
2. B. 18 (Correct answer)
3. C. 27
4. D. 16

Correct Answer

Option B — 18

Detailed Solution & Explanation

The correct answer is 18.

Key Points

• When two numbers are in a fixed ratio, express them as multiples of a common factor.
• Let the two numbers be 2x and 11x.
• The difference between them is given as 81:
• 11x − 2x = 81 → 9x = 81 → x = 9.
• So the two numbers are 2x = 18 and 11x = 99.
• The smaller number is 18.
• Quick check: 99 − 18 = 81 ✓ and 18 : 99 = 2 : 11 ✓.
• in any ratio problem, the phrase 'ratio 2 : 11' means the numbers share a common multiplier — always convert to 2x, 11x and use the extra condition (difference, sum, or product) to find x.

Exam Tip

• the difference of the ratio terms (here 11 − 2 = 9) always corresponds to the given numerical difference, so 1 part = 81 ÷ 9 = 9 — a one-line shortcut for such questions.