Question
The present ages of R and S are in the ratio 5:6. 3 years
back, the average age of R, S, and T was 33 years. R was 12 years younger than T at that time. What will be T’s age 7 years from now?Solution
ATQ,
Let current ages be: R = 5x, S = 6x, T = y
3 years ago: 5x–3, 6x–3, y–3
ATQ,
(5x–3 + 6x–3 + y–3) = 3 × 33
⇒ 11x + y – 9 = 99
⇒ 11x + y = 108 ---------- (I)
Also,
5x – 3 = y – 3 – 12
⇒ 5x = y – 12
⇒ y – 5x = 12 ---------- (II)
Subtracting (II) from (I):
11x + y – (y – 5x) = 108 – 12
⇒ 16x = 96
⇒ x = 6
Then y = 5x + 12 = 30 + 12 = 42
∴ T’s age after 7 years = 42 + 7 = 49 years
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