Question

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.

Answer 1

Let the present age of the man be M years and his son's age be 5 years. Then, as per the question description, 

M + 5 = 45 ...... (i) 

{M - 5)(5 - 5) = 124 ...... (ii) 

From (i), we get: M=45-5 ...... (iii) 

Putting (iii) in (ii), we get: {45 - 5 - 5) (5 - 5) = 124 

⇒  (40 - 5)(5 - 5) =124

⇒ S² - 45 S + 324 = 0

⇒ S² - 9S - 36S + 324 = 0

⇒ S (5 - 9) - 36(5 - 9) = 0 

⇒ S = 9 , 36

⇒ S = 9 years and  hence , M = 36 years