The sum of the ages of a father and son is 45 years. Five years ago the product of their ages was 4 times the father's age at that time. the present ages of the father's and son respectively are?

25 years, 10 years
36 years, 9 years
39 years, 6 years
None of these

Correct Answer: 36 years, 9 years

Explanation:

Let the present age of the father and son be x years and (45 - x)years respectively.
Then, (x - 5)(45 - x - 5) = 4(x - 5)
⇒ -x² + 41x - 180 = 0
⇒ (x - 5)(x - 36) = 0
⇒ x = 36
∴ The present ages of father and son are 36 years and 9 years respectively.

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