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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.
Solution
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
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