Question

The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as his father. What are their ages now ?

Answer 1

Sum of ages of Anup and his father = 100 years

Let present age of Anup = x years

$\therefore$ Age of his father = (100 - x) years

$\therefore$ Age of Anuj $=\frac{100-x}{5}$ years and also Anuj's age = (x + 8) years ....I

$\because$ Anup becomes as old as his father is now after (100 - 2x) years

$\therefore$ After (100- 2x)years

Anuj's age $=(\frac{100-x}{5}+100-2x)$

$\frac{600-11x}{5}$ ....II

From I and II,

$\frac{600-11x}{5}=x+8\Rightarrow 600-11x=5x+40$

$\Rightarrow 5x+11x=600-40\Rightarrow 16x=560$

$\Rightarrow x=\frac{560}{16}=35$

$\therefore$ Present age of Anup = 35 years and his father's age = 100 - 35 = 65 years and his son's age $=\frac{100-35}{5}$ years

$=\frac{65}{5}=13$ years