Question

The age of a man is $3$ times that of his son. $15$ years ago, the man was $9$ times as old as his son. What will be the age of man after $15$ years?

• A. $60$ years
• B. $80$ years
• C. $75$ years
• D. $105$ years

Answer 1

Answer: (C)

$75$ years

Let the age of the son be $x$ years.

Then, age of man $=3x$ years.
$15$ years ago, son's age was $(x-15)$ years,
and man's age was $(3x-15)$ years.
Given, $(3x-15)=9(x-15)$
$\Rightarrow 3x-15=9x-135\Rightarrow 9x-3x=135-15$
$\Rightarrow 6x=120\Rightarrow x=\frac{120}{6}=20$
$\therefore$ son's present age $=20$ years
and man's present age $=60$ years
Hence, the man's age after $15$ years $=(60+15)$ years $=75$ years.