This problem involves calculating ages based on a specific relationship described by the father. The key is understanding that the age difference between the father and son remains constant.

Father Son Age Logic

Let $F$ represent the father's current age and $S$ represent the son's current age.

• We are given the father's current age: $F = 52$ years.

Analyzing the Statement

The father's statement is: "I was as old as you are when I became your father."

• "When I became your father" refers to the time when the son was born.
• This was $S$ years ago (the son's current age).
• Therefore, the father's age at that time was $F - S$.
• The statement sets up the equation: Father's age then = Son's age now.
• So, $F - S = S$.

Calculating Son's Current Age

Substitute the father's current age ($F = 52$) into the equation:

$ 52 - S = S $

To solve for $S$, add $S$ to both sides:

$ 52 = S + S $

$ 52 = 2S $

Divide by 2:

$ S = \frac{52}{2} $

$ S = 26 $

The son's current age is 26 years.

Finding Son's Future Age

The question asks for the son's age after 10 years.

Son's age after 10 years = Son's current age + 10 years

$ \text{Son's age after 10 years} = 26 + 10 $

$ \text{Son's age after 10 years} = 36 \text{ years} $

The son's age after 10 years will be 36 years.