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
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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