### 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.

A. 8 years

B. 12 years

C. 15 years

D. 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 $\begin{array}{l}=\left(\Large\frac{60-48}{3}\right)\\ =\Large\frac{12}{3}\\ =4\text{ years }\end{array}$ 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 $\begin{array}{l}=\left(\Large\frac{80-60}{4}\right)\\ =5\text{ years }\end{array}$ 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 $\begin{array}{l}=\left(\Large\frac{90-80}{5}\right)\\ =2\text{ years }\end{array}$ 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 $\begin{array}{l}=\left(\Large\frac{90-90}{6}\right)\text{ years }\\ =1\text{ year }\end{array}$ Hence, the present age of the eldest son = (11 + 1) years = 12 years