Question

A man’s age is six times the age of his son. In six years, the father’s age will be three times of the son’s age. The age of the father and the son are respectively:
A. 18 years and 3 years
B. 30 years and 5 years
C. 24 years and 4 years
D. 42 years and 7 years

Answer 1

Hint: Here in this question we will proceed by assuming the present age of the son be $x$. So, the present age of the man will be $6x$ as given in the question that man’s age is six times the age of his son. Then we will convert the given information that in six years, the father’s age will be three times of the son’s age into equations and solve these equations to get the answer.

Complete step by step answer:
We have given that a man’s age is six times the age of his son.
Let us assume that the son’s present age is $x$. So, the present age of the father will be $6x$.
Also, we have given that in six years, the father’s age will be three times of the son’s age.
So, after six years the age of the father will be $6x+6$ and the age of the son will be $x+6$.
As we have given that the father’s age will be three times of the son’s age. So, we multiply the age of the son by $3$ and equate it with the age of the father.
We get $6x+6=3\left( x+6 \right)$
Simplify further we get,
$\begin{align}
  & \Rightarrow 6x+6=3x+18 \\
 & \Rightarrow 6x-3x=18-6 \\
 & \Rightarrow 3x=12 \\
 & \Rightarrow x=4 \\
\end{align}$
So, the present age of the son is $4$ years.
The present age of a father is $6x=6\times 4=24$ years.
Option C is the correct answer.

Note: The point to be noted is that we have to assume the age of son to be $x$. We can also verify our answer by using the information given in the question that in six years, the father’s age will be three times of the son’s age.
Present age of the son is $4$ years and the present age of the father is $24$ years.
So, after six years the age of the son will be $10$ years and the age of the father will be $30$ years, which is three times of the son’s age. It means our answer is correct.