10 years ago, the average age of a family consisting of 4 members was 24 years. Two children having been born (with age difference of 2 years), the present average age of the family is the same. What is the present age of the youngest child?

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5 years

3 years

2 years

1 year

answer is C.

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Detailed Solution

Given that 10 years ago, the average age of a family consisting of 4 members was 24 years

Suppose that the ages of two new children is $x, x + 2$

Given that

$\begin{array}{rcl} \frac{4 (24 + 10) + x + x + 2}{6} & = & 24 \\ 2 x + 2 + 40 & = & 2 (24) \\ x + 1 + 20 & = & 24 \\ x & = & 3 \end{array}$

Therefore, the age of youngest child is $3$

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