Question : The average age of A and B is 20 years. If A is to be replaced by C, the average would be 19 years. The average age of C and A is 21 years. The ages of A, B, and C in order (in years) are:
Option 1: 18, 22, and 20
Option 2: 18, 20, and 22
Option 3: 22, 18, and 20
Option 4: 22, 20, and 18
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Correct Answer: 22, 18, and 20
Solution : Given: The average age of A and B = 20 years If A is to be replaced by C, the average would be 19 years. The average age of C and A = 21 years So, $\frac{A+B}{2}$ = 20 ⇒ A + B = 40 years ------(1) $\frac{A+C}{2}$ = 21 ⇒ A + C = 42 years ------(2) If A is replaced by C, then, $\frac{B + C}{2}$ = 19 ⇒ B + C = 38 years ------(3) Add equation (1), (2) and (3) (A + B) + (A + C) + (B + C) = 40 + 42 + 38 ⇒ A + B + C = 60 -------(4) Subtract equation (1) from (4) (A + B + C) – (A + B) = 60 – 40 ⇒ C = 20 years Subtract equation (2) from (4) (A + B + C) – (A + C) = 60 – 42 ⇒ B = 18 years Subtract equation (3) from (4) (A + B + C) – (B + C) = 60 – 38 ⇒ A = 22 years Hence, the correct answer is 22, 18, and 20.
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