Ages (birth-time equality statement): A father says, “I was as old as you are now at the time of your birth.” If the father is 38 now, how old was the son five years ago?

Introduction / Context:
The statement implies that the current difference between father and son equals the son's current age: at the son's birth, the father's age equaled today's son's age. This unlocks the ages immediately without heavy algebra.

Given Data / Assumptions:
Let father's present age be F = 38 and son's present age be S. The statement gives F − S = S ⇒ F = 2S.

Concept / Approach:
Solve for S from F = 2S, then roll back five years to answer the question asked.

Step-by-Step Solution:

Verification / Alternative check:
At the time of birth (19 years ago), father's age would have been 38 − 19 = 19, which equals the son's current age—matching the statement (✓).

Why Other Options Are Wrong:
They contradict F = 2S or fail the five-years-ago rollback.

Common Pitfalls:
Interpreting “was as old as you are now” as “twice as old” or some other multiplier; it is an equality with the son's present age.

Final Answer:
14 years