Question
The present ages of Aman and Rehan are in ratio 3:5. 5
years ago, the average age of Aman, Rehan and Tarun was 28 years. Aman was 11 years younger than Tarun at that time. Find Tarun's age 7 years hence.Solution
ATQ,
Let present ages = 3x, 5x, y
5 yrs ago: 3x–5, 5x–5, y–5
(3x–5 + 5x–5 + y–5) = 84
⇒ 8x + y – 15 = 84 ⇒ 8x + y = 99 ...(I)
Also, 3x = y – 11 ⇒ y – 3x = 11 ...(II)
(I) – (II): 8x + y – y + 3x = 99 – 11 ⇒ 11x = 88 ⇒ x = 8
Then y = 3x + 11 = 24 + 11 = 35
Tarun’s age 7 years hence = 42 years
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