The sum of the present ages of a father and his son is 60 years.\nFive years ago, the father's age was four times the age of the son.\nWhat is the present age of the son?

Introduction / Context:
This is a typical linear age puzzle connecting the sum of present ages with a multiplicative relationship in the past. You must use both pieces of information to form a system of equations to find the present age of the son.

Given Data / Assumptions:

• Present age of father = F years.
• Present age of son = S years.
• F + S = 60.
• Five years ago the father was four times as old as the son.
• We need to find S.

Concept / Approach:
Five years ago, their ages were F - 5 and S - 5. The condition can be written as: F - 5 = 4(S - 5). We then use the equation F + S = 60 to express F in terms of S or vice versa and substitute into the second equation. This produces a linear equation in one variable which we solve.

Step-by-Step Solution:
From the sum condition: F + S = 60. So F = 60 - S. Five years ago: F - 5 = 4(S - 5). Substitute F = 60 - S into the second equation. (60 - S) - 5 = 4(S - 5). 55 - S = 4S - 20. Bring terms together: 55 + 20 = 4S + S. 75 = 5S. S = 15. Therefore, the son is 15 years old at present.

Verification / Alternative check:
If S = 15, then F = 60 - 15 = 45. Five years ago, the son was 10 and the father was 40. The father s age was 40, which is four times 10, matching the given condition precisely. This confirms that S = 15 is correct.

Why Other Options Are Wrong:
If S were 5, 10 or 20, substituting into the sum equation would give father ages of 55, 50 or 40 respectively. Then the past relationship F - 5 = 4(S - 5) would not hold. Only S = 15 simultaneously satisfies both conditions.

Common Pitfalls:
Learners sometimes forget to apply the past condition to both ages (subtracting 5 from only one of them). Another common mistake is to mis-handle the algebra when substituting and rearranging. Writing each step clearly and simplifying slowly reduces these errors.

Final Answer:
The present age of the son is 15 years.