Question

The father’s age is six times his son’s age. Four years from now, the age of the father will be four times his son’s age. The present ages (in years) of the father and the son respectively are ___.

• A. 60 years, 10 years
• B. 36 years, 6 years
• C. 30 years, 5 years
• D. 24 years, 4 years

Answer 1

The correct option is B 36 years, 6 years

Let $x$ years and $y$ years represent the ages of the father and the son respectively. Then, we have $x=6y...\left(1\right)$
Four years from now, the father's age will be $x+4$ years and the son's age will be $y+4$ years.
Thus, we have $x+4=4(y+4)$
$\Rightarrow x–4y=12...\left(2\right)$
Substituting the value of $x$ from (1) in (2), we have
$6y–4y=12⟹2y=12⟹y=6$.
Since $x=6y$, we have $x=36$.
Hence, the present ages of the father and the son are 36 years and 6 years respectively.