The sum of the present ages of a father and his son is 60 years. Six years ago, the age of the father was five times the age of the son. What will be the age of the son after 6 years?

Introduction / Context:
This is a classic problem on the ages of a father and son. We are given their total present age and a relationship between their ages six years ago. Using this information, we can determine their individual present ages and then find the son's age after 6 more years. Such questions are common in aptitude exams and test the ability to form and solve linear equations from word statements.

Given Data / Assumptions:
- The sum of the present ages of the father and his son is 60 years.
- Six years ago, the father's age was five times the son's age.
- Ages are in years.
- We must find the son's age after 6 years from now.

Concept / Approach:
We assign variables to the present ages of the father and the son. The given total age at present provides one equation. The condition from six years ago gives another equation relating their ages at that time. Solving this system of two linear equations yields the present ages. Finally, we add 6 years to the son's present age to answer the question.

Step-by-Step Solution:
Step 1: Let the present age of the father be F years and the present age of the son be S years.Step 2: The sum of their present ages is F + S = 60.Step 3: Six years ago, the father was F - 6 years old and the son was S - 6 years old.Step 4: The problem states that six years ago the father's age was five times the son's age, so F - 6 = 5 * (S - 6).Step 5: Expand the second equation: F - 6 = 5S - 30, which gives F = 5S - 24.Step 6: Substitute F = 5S - 24 into F + S = 60 to obtain (5S - 24) + S = 60.Step 7: Combine terms to get 6S - 24 = 60, so 6S = 84 and S = 84 / 6 = 14 years.Step 8: The son is currently 14 years old, so after 6 years his age will be 14 + 6 = 20 years.

Verification / Alternative check:
If the son is 14 years old now, then the father's age is F = 60 - 14 = 46 years. Six years ago, the son was 8 years old and the father was 40 years old. The ratio 40:8 equals 5:1, so the father's age was indeed five times the son's age at that time. This confirms that the ages are consistent with the given information and that the son will be 20 years old after 6 years.

Why Other Options Are Wrong:
If the son's age after 6 years were 25, 33, 45, or 26 years, then his present age would be 19, 27, 39, or 20 years respectively. Substituting these values into the total and ratio conditions either breaks the sum of 60 years or violates the five times relation from six years ago. Therefore, none of those options can satisfy all the constraints simultaneously.

Common Pitfalls:
Some learners mistakenly set F = 5S directly instead of applying the condition six years ago, which leads to incorrect equations. Others forget to subtract 6 from both ages when working with the past condition. It is important to pay attention to time phrases such as "six years ago" and to adjust both ages accordingly before applying the ratio or multiple condition.

Final Answer:
The son will be 20 years old after 6 years.