A. 8 years

B. 12 years

C. 15 years

D. 16 years

Show Answer

### Solution(By Apex 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 $\begin{array}{l}=\left(\Large\frac{60-48}{3}\right)\\ =\Large\frac{12}{3}\\ =4\text{ years }\end{array}$ 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