Question : 5 years ago the average age of a family which includes a father, a mother, and a son was 35 years. 3 years ago the average age of father and mother was 46 years. What is the present age (in years) of the son?
Option 1: 20
Option 2: 24
Option 3: 26
Option 4: 22
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Correct Answer: 22
Solution :
Let the ages of the father, mother, and son be 5 years ago $F$, $M$, and $S$ respectively.
The average age of the father, mother, and son was 35 years.
$\frac{(F) + (M) + (S)}{3} = 35$
⇒ $F + M + S = 105$
3 years ago, the average age of the father and mother was 46 years.
$\frac{(F+2) + (M+2)}{2} = 46$
⇒ $F + M = 88$
The present age of the son = 105 – 88 + 5= 22 years
Hence, the correct answer is 22.
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