Question

5 years ago, the age of a man was 7 times the age of his son. The age of the man will be 3 times the age of his son in 5 years from now. How old are the man and his son now?

Answer 1

Let the present age of the son be x years.
Then, the man's present age = y years.
5 years ago, their ages were
(x - 5) and (y - 5) respectively.
As per given conditions,

`((x - 5))/((y - 5)) = (1)/(7)`
⇒ 7x - 25 = y - 5
⇒ 7x - y = 30----(1)
Also, 5 years hence, their ages are
(x + 5) and (y + 5) respectively.
Given, The age of the man will be 3 times the age
of his son in 5 years from now.
⇒ (y + 5)= 3(x + 5)
⇒ y - 3x = 10----(2)
Adding (1) and (2), we get:
4x = 40
⇒ x = 10 years.
⇒ y = 3x + 10
= 30 + 10
= 40 years.
Thus, the present age of the son is 10 years.
Then, the man's age = 40 years.