Explanation:

The family consists of grandparents, parents and three grandchildren.
So, the number of family members = 2 + 2 + 3 = 7
We know,
Average of quantities = Sum of quantities /No. of quantities
The average age of the grandparents is 70 years.
So, the total age of the grandparents = 70 × 2 = 140 years
The average age of the parents is 40 years.
So, the total age of the parents = 40 × 2 = 80 years
The average age of the grandchildren is 10 years.
So, the total age of the grandchildren = 10 × 3 = 30 years
∴  The total age of the family members = 140 + 80 + 30 = 250 years.
∴  The average age of the family = 250 /7 = 35 5/7 yrs