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

Solution(By Examveda Team)

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