Question

The father's age is six times his son’s age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father are respectively.
A. 4 and 24
B. 5 and 30
C. 6 and 36
D. 3 and 24

Answer 1

Hint: In the given question take the present age of father and his son as variables. Then equate father's age to six times his son's age. Then add four years to the father's and his son's age and multiply his son's age with four and equate with father’s age. Then you will obtain two equations. By solving them we can obtain the present age of father and his son.

Complete step-by-step answer:
Let the present age of father be \[x\] years and the present age of son be \[y\] years.
Given that the father’s age is six times his son’s age i.e., \[x = 6y...........\left( 1 \right)\]
Since, the age of the father will be four times his son's age after four years, we have
\[ \Rightarrow x + 4 = 4\left( {y + 4} \right)............\left( 2 \right)\]
Substituting equation (1) in (2) we get,
$   \Rightarrow 6y + 4 = 4\left( {y + 4} \right) $
$   \Rightarrow 6y + 4 = 4y + 16 $

On simplification,
$   \Rightarrow 6y - 4y = 16 - 4 $

Simplifying further,
$   \Rightarrow 2y = 12 $

Dividing on both sides by 2, we get
$  y = 6 $
From equation (1) we have
$ \Rightarrow x = 6y $

Substituting the $y$ value in the above equation,
$   \Rightarrow x = 6 \times 6 $

On simplification we get
$ x = 36 $
Therefore, the present age of father is 36 years and the present age of his son is 6 years.
Thus, the correct option is C. 6 and 36

Note: The age of the son cannot be more than the age of his father i.e., \[x > y\]. And the age of both of them cannot be less than four, because in the given problem the condition period has already passed away four years.