Question

Two years ago, a father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Find their present age?

Answer 1

Hint: In order to solve this question, we must assume the age of the son as a variable so that it can be expressed in mathematical form or equation which will also be helpful to find the relation between both persons. Using this equation we can solve this problem.

Complete step-by-step answer:
Let us consider age of son be x years
According to the question
First condition-
Two years ago son’s age would be x-2 and father’s age would be 3(x-2)
$\therefore $ The present age of father would be
3x-6+2=3x-4
 Second condition-
Two years hence father’s age will be
3x-4+2=3x-2
Two years hence son’s age will be x+2
 Also given that,
Twice his age will be equal to five times that of his son i.e.
 5$ \times $ (x+2)=2$ \times $ (3x-2)
 $ \Rightarrow $ 5x+10=6x-4
 $ \Rightarrow $ x=14

As we considered age of son be x which is son’s present age 14 years
Father’s present age is
(3$ \times $ 14)-4=38 years

Note: To solve this type of question, other ways can also be used. We can use two variables in place of one so that it will form two equations where we can apply elimination method, substitution method. Thus in a way we get our desired answer.