A man is 24 years older than his son. In two years, the age of the man will be twice the age of his son at that time. What is the present age of the son?

Introduction / Context:
This is a straightforward problems-on-ages question involving a fixed age difference between a father and his son. The situation also provides a future condition relating their ages. The goal is to form a simple linear equation and solve it to find the present age of the son.

Given Data / Assumptions:

• The man is currently 24 years older than his son.
• After 2 years, the man will be twice as old as his son.
• We are asked to find the present age of the son.
• All ages are measured in years and are assumed to be positive.

Concept / Approach:
The key idea is to express both ages using a single variable. The difference between their ages remains constant over time. A condition involving their ages after 2 years leads to a linear equation that can be solved for the son age. Once we know the son age, we can confirm the father age and verify the condition.

Step-by-Step Solution:
Let the present age of the son be S years.Then the present age of the man (father) is S + 24 years.After 2 years, the son age will be S + 2, and the father age will be S + 24 + 2 = S + 26.The problem states that after 2 years, the father age will be twice the son age: S + 26 = 2 * (S + 2).Expand the right side: S + 26 = 2 * S + 4.Rearrange: S + 26 = 2 * S + 4 implies 26 - 4 = 2 * S - S.So 22 = S.Therefore the present age of the son is 22 years.

Verification / Alternative check:
If the son is 22 years old now, the father is 22 + 24 = 46 years old now.After 2 years, the son will be 24 and the father will be 48.Check the condition: 48 is indeed 2 times 24.Hence the solution S = 22 years satisfies all the given conditions.

Why Other Options Are Wrong:
20 years: If the son is 20, the father is 44, and after 2 years they will be 22 and 46; 46 is not twice 22.21 years: If the son is 21, the father is 45, and after 2 years they will be 23 and 47; 47 is not twice 23.23 years: If the son is 23, the father is 47, and after 2 years they will be 25 and 49; 49 is not twice 25.

Common Pitfalls:
Some students mistakenly set up the equation using current ages instead of future ages, which gives a wrong relationship.Another error is misreading the phrase twice the age and incorrectly writing 2 * S + 2 instead of 2 * (S + 2).Forgetting that the age difference remains 24 years at all times can also lead to confusion.

Final Answer:
The present age of the son is 22 years.