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

Introduction / Context:
This mixes a present sum condition with a past product condition. The structure simplifies after factoring the past product equation.

Given Data / Assumptions:

• Present ages: Father = f, Son = s
• f + s = 45
• Five years ago: (f − 5)(s − 5) = 4(f − 5)

Concept / Approach:
Factor the past equation by taking (f − 5) common. This yields two possible cases; reject the infeasible one and use the sum to find both ages.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 25,10 and 39,6 do not satisfy both conditions.
• None of these and 28,17 are inconsistent with the factored constraint.

Common Pitfalls:
Missing the factorization shortcut; choosing f = 5 despite being unrealistic; or misapplying the 5-year shift to only one age.

Final Answer:
36 years, 9 years