Question

A man is 24 years older than his son. 12 years ago, he was five times as old as his son. Find the present ages of both.

• A. Present age of father is $44$ years and Present age of son is $20$ years
• B. Present age of father is $42$ years and Present age of son is $18$ years
• C. Present age of father is $60$ years and Present age of son is $36$ years
• D. Present age of father is $48$ years and Present age of son is $24$ years

Answer 1

Answer: (B)

Present age of father is $42$ years and Present age of son is $18$ years

Let the present age of the father be $x$ years and the present age of the son be$y$ years.

It is given that the man is $24$ years older than his son that is:

$x=y+24$

$\Rightarrow x-y=24..........\left(1\right)$

Also, $12$ years ago, he was five times as old as his son that is:

$(x-12)=5(y-12)$

$\Rightarrow x-12=5y-60$

$\Rightarrow x-5y=-60+12$

$\Rightarrow x-5y=-48.......\left(2\right)$

On subtracting $\left(1\right)$ from $\left(2\right)$, we get:

$(x-x)+(-5y+y)=-24-48$

$\Rightarrow -4y=-72$

$\Rightarrow y=18$

Substituting this value of $y$ in $\left(1\right)$, we get:

$x-18=24$

$\Rightarrow x=24+18=42$

Hence, the present age of the father is $42$ years and the present age of the son is$18$ years.