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 ears. What is the average age of the family? 

Given that a family consists of two grandparents, two parents and three grandchildren. 

• The average age of the grandparents is 67 years, 
• The average age of the parents is 35 years 
• The average age of the grandchildren is 6 years

There are 7 persons in the family. To get the average age of family members, use the concept of weighted mean.

It implies that 

  $\begin{array}{rcl}Avg& =& \frac{2\left(67\right)+2\left(35\right)+3\left(6\right)}{7}\\ & =& \frac{134+70+18}{7}\\ & =& \frac{222}{7}\\ & =& 31.71\end{array}$

Therefore, the average age of the family is $\boxed{\mathbf{31}\mathbf{.}\mathbf{71}}$