Question
Present ages of ‘P’ and ‘Q’ are in ratio 1:2. 4
years ago, the average of the ages of P, Q and R was 26 years. At that time, P was 10 years younger than R. What will be the age of R after 8 years?Solution
ATQ,
Let present ages of P, Q and R be x, 2x, and y respectively.4 years ago: x–4, 2x–4, y–4.
ATQ,
(x–4 + 2x–4 + y–4) = 3 × 26
⇒ 3x + y – 12 = 78
⇒ 3x + y = 90 ---------- (I)
Also,
x – 4 = y – 4 – 10
⇒ x = y – 10
⇒ y – x = 10 ---------- (II)
Sub (II) in (I):
3x + (x + 10) = 90
⇒ 4x = 80
⇒ x = 20
Then y = 30
∴ R’s age after 8 years = 30 + 8 = 38 years
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