Mr. Joe’s family consists of six people-himself, his wife and ir four children. It is known that average age of family immediately after birth of first, second, third and fourth child was 16, 15, 16 and 15 years respectively. Find age of Mr. Joe’s eldest son if present average age of entire family is 16 years -

When the first child was born, the total age of all the family members
= (16 × 3) years
= 48 years
When the second child was born, the total age of all the family members
= (15 × 4) years
= 60 years
By the time the second child was born, each one of the 3 family members had grown by
$$\eqalign{ & = \left( {\frac{{60 - 48}}{3}} \right) \cr & = \frac{{12}}{3} \cr} $$
= 4 years
Hence, the age of eldest son when the second child was born = 4 years
When the third child was born, the total age of all the family members
= (16 × 5) years
= 80 years
By the time, the third child was born, each one of the four family members had grown by
= $$\left( {\frac{{80 - 60}}{4}} \right)$$
= 5 years
So, the age of the eldest son when the third child was born
= (4 + 5) years
= 9 years
When the fourth child was born, the total age of all the family members
= (15 × 6) years
= 90 years
By the time, the fourth child was born, each of the five family members had grown by
= $$\left( {\frac{{90 - 80}}{5}} \right)$$
= 2 years
So, the age of the eldest son when the fourth child was born
= (9 + 2) years
= 11 years
At present, the total age of all the 6 family members
= (16 × 6) years
= 96 years
By now, each one of the 6 members have grown by
= $$\left( {\frac{{96 - 90}}{6}} \right)$$  years
= 1 year
Hence, the present age of the eldest son
= (11 + 1) years
= 12 years