Problems on Ages — “At present, a father is 30 years older than his only son. What was the father’s age when the son was born?”

Introduction / Context:
The wording asks for the father’s age at the son’s birth. If a father is currently a fixed number of years older than his child, then at the time of birth that difference equals the father’s age (since the child’s age was zero).

Given Data / Assumptions:

• Let son = S now; father = S + 30 now.
• At birth (S years ago): father’s age = (S + 30) − S.
• We assume normal, nonnegative ages.

Concept / Approach:
Age differences remain constant over time. At the child’s birth the child’s age is 0, so the difference equals the parent’s age then. No algebra beyond that idea is required.

Step-by-Step Solution:

Verification / Alternative check:
If the son were, say, 12 today, father would be 42. Twelve years ago (at birth) father would have been 30. Works for any S since the difference is constant.

Why Other Options Are Wrong:
25/28/35/40 are inconsistent with the invariant 30-year difference evaluated at the moment of birth.

Common Pitfalls:
Subtracting the difference from 30 or adding extra steps; overcomplicating a straightforward difference-invariance property.

Final Answer:
30 years