Question

A father is three times as old as his son. After 12 years, his age will be twice as that of his son then find their present ages?

Answer 1

Hint: In this question, first of all, we will consider the present ages of the father and his son as variables. Then using the given data, we will obtain two equations in terms of the variables. By solving both the equations we obtain our required answer.

Complete step-by-step solution:
Let the present ages of father and his son be \[x\] and \[y\].
Given that father is three times as old as his son i.e., \[x = 3y...................\left( 1 \right)\].
After 12 years the age of father = \[x + 12\]
And after 12 years the age of his son = \[y + 12\]
Given that after 12 years father`s age will be twice as that of his son.
So, we have \[x + 12 = 2\left( {y + 12} \right)..............................\left( 2 \right)\]
From equation (1) and (2), we have
\[ \Rightarrow 3y + 12 = 2\left( {y + 12} \right) \\
   \Rightarrow 3y + 12 = 2y + 24 \\
   \Rightarrow 3y - 2y = 24 - 12 \\
  \therefore y = 12 \]
Substituting \[y = 12\] in equation (1), we get
\[ \Rightarrow x = 3\left( {12} \right) \\
  \therefore x = 36 \]
Thus, the present age of the son is 12 years and the present age of the father is 36.

Note: Since, the age of the father is thrice that of his son, the obtained age of the father should always greater than the age of his son. In these kinds of questions, the values of the variables should not be negative as age doesn’t go to a negative value.