Question
Present age ratio of P and Q is 1:2. Four years ago,
average age of P, Q, and R was 32 years. At that time, P was 24 years younger than R. What will be R’s age after 5 years?Solution
ATQ,
Let present ages of P, Q, and R be x, 2x, and y respectively. Four years ago: P → x – 4, Q → 2x – 4, R → y – 4 According to question: (x – 4 + 2x – 4 + y – 4) = 3 × 32 ⇒ 3x + y – 12 = 96 ⇒ 3x + y = 108 -------- (i) Also: y – 4 – (x – 4) = 24 ⇒ y – x = 24 -------- (ii) Subtracting (ii) from (i): (3x + y) – (y – x) = 108 – 24 ⇒ 3x + y – y + x = 84 ⇒ 4x = 84 ⇒ x = 21 Put x = 21 in equation (i): 3x + y = 108 ⇒ 63 + y = 108 ⇒ y = 45 R’s age after 5 years = 45 + 5 = 50 years
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