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1. 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. $28 \frac{4}{7}$ years

B. $31 \frac{5}{7}$ years

C. $32 \frac{1}{7}$ years

D. None of these

Solution:

\begin{aligned} Required average \\ = \frac{67 \times 2 + 35 \times 2 + 6 \times 3}{2 + 2 + 3} \\ = \frac{134 + 70 + 18}{7} \\ = \frac{222}{7} \\ = 31 \frac{5}{7} years \end{aligned}

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