The present ages of A, B and C are in proportions 4:5:9. Nine years ago, sum…
2024
The present ages of A, B and C are in proportions 4:5:9. Nine years ago, sum of their ages was 45 years. Find their present ages in years.
Answer: D. 16, 20, 36 — Answer: 16, 20, 36 Explanation: Let the present ages of A, B and C be 4x, 5x and 9x respectively. Nine years ago their ages were 4x - 9, 5x - 9 and 9x - 9.…
- A.
15, 20, 35
- B.
20, 24, 36
- C.
20, 25, 45
- D.
16, 20, 36
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Show answer & explanation
Correct answer: D
Answer: 16, 20, 36
Explanation:
Let the present ages of A, B and C be 4x, 5x and 9x respectively.
Nine years ago their ages were 4x - 9, 5x - 9 and 9x - 9. The given condition says the sum then was 45, so:
(4x - 9) + (5x - 9) + (9x - 9) = 45
Simplify the equation: 4x + 5x + 9x - 27 = 45 ⇒ 18x - 27 = 45 ⇒ 18x = 72 ⇒ x = 4.
Therefore the present ages are 4x = 16, 5x = 20 and 9x = 36 years.
Quick check:
Present sum = 16 + 20 + 36 = 72. Subtracting 9 from each person reduces the total by 27, giving 72 - 27 = 45, which matches the condition.
The ratio 16:20:36 simplifies to 4:5:9, as required.