Question

A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time?
(A) 13 years
(B) 18 years
(C) 14 years
(D) 19 years

Answer 1

Hint: Assume that after x years from now, the age of the son will be half the age of the man at that time. The present age of man and his son is 42 years and 12 years respectively. After x years the age of the man and his son both will be x years more of their present ages. The age of man and his son after x years is \[\left( 42+x \right)\] years and \[\left( 12+x \right)\] years respectively. It is given that the son's age is half of the age of the man. Use this information and form the equation. Now, solve it further and get the value of x.

Complete step by step answer:
According to the question, it is given that a man is 42 years old and his son is 12 years old.
The present age of man = 42 years ………………….(1)
The present age of son = 12 years ………………….(2)
Let us assume that after x years from now, the age of the son will be half the age of the man at that time.
After x years the age of the man and his son both will be x years more of their present ages.
From equation (1) and equation (2), we have the present ages of the man and his son.
The age of man after x years = \[\left( 42+x \right)\] years ………………………….(3)
The age of son after x years = \[\left( 12+x \right)\] years ………………………….(4)
From equation (3) and equation (4), we have the age of man and his son.
It is given that the son's age is half of the age of the man. So,
\[\begin{align}
  & \Rightarrow \dfrac{\left( 42+x \right)}{2}=\left( 12+x \right) \\
 & \Rightarrow \left( 42+x \right)=2\left( 12+x \right) \\
 & \Rightarrow \left( 42+x \right)=24+2x \\
 & \Rightarrow 42-24=2x-x \\
 & \Rightarrow 18=x \\
\end{align}\]
So, after 18 years, the age of the son will be half the age of the man at that time.
Hence, option (B) is the correct one.

Note: We can also solve this question by observing the options given.
In option (A), we have 13 years. That is,
The age of man after 13 years = \[\left( 42+13 \right)\] years = 55 years
The age of son after 13 years = \[\left( 12+13 \right)\] years = 25 years
The age of the son is not half of the man’s age. So, this option is incorrect.
In option (B), we have 18 years. That is,
The age of man after 18 years = \[\left( 42+18 \right)\] years = 60 years.
The age of son after 18 years = \[\left( 12+18 \right)\] years = 30 years.
The age of the son is exactly equal to half of the man’s age. So, this option is correct.
Hence, option (B) is the correct one.