Question : The average age of a husband and his wife 3 years ago was 39 years. The average age of the husband, wife, and child is 2 years hence will be 34 years. Find the present age of the child.
Option 1: 12 years
Option 2: 16 years
Option 3: 15 years
Option 4: 18 years
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Correct Answer: 12 years
Solution : Let the present ages of the husband, wife, and child be $H$, $W$, and $C$ respectively. From the problem, we know that the average age of the husband and wife 3 years ago was 39 years. $⇒\frac{(H-3) + (W-3)}{2}$ = 39 $⇒H + W = 84$ ___(1) Given that the average age of the husband, wife, and child 2 years from now will be 34 years. $⇒\frac{(H+2) + (W+2) + (C+2)}{3}$ = 34 $⇒H + W + C = 96 $ ___(2) Subtracting equation (1) from equation (2) gives, $⇒C = 96 - 84 = 12$ Hence, the correct answer is 12 years.
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