Question

A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is $67$ years, that of the parents is $35$ years and that of the grandchildren is $6$ years. What is the average age of the family?

• A. $28\frac{4}{7}\mathrm{years}$
• B. $31\frac{5}{7}\mathrm{years}$
• C. $32\frac{1}{7}\mathrm{years}$
• D. None of these

Answer 1

The correct option is B

$31\frac{5}{7}\mathrm{years}$

Explanation of the correct option

$\begin{array}{rcl}\mathrm{Required}\mathrm{average}& =& \frac{2\times 67+2\times 35+3\times 6}{2+2+3}\\ & =& \frac{134+70+18}{7}\\ & =& \frac{222}{7}\\ & =& 31\frac{5}{7}\end{array}$

Therefore, the average age of the family is $31\frac{5}{7}\mathrm{years}$.

Hence, Option (B) is correct.