The average age of A and B is 17 years. If A is to be replaced by C, the average would be 16 years. The average age of C and A is 18 years. Find the age of A.

A + B = 2 × 17 = 34 yr B + C = 2 × 16 = 32 yr C + A = 2 × 18 = 36 yr On adding all three, 2 (A + B + C) = 34 + 32 + 36 = 102 ⇒ A + B + C = 51 ∴ A = (A + B + C) – (B + C) = 51 – 32 = 19 yr

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