Problems on Ages — “Mother is now three times the daughter’s age; father is 5 years older than mother. The daughter is 10. What was the father’s age when the daughter was born?”

Introduction / Context:
We are asked for a past age (“when the daughter was born”) given current multiplicative and offset relations. Determine current ages first, then subtract the daughter’s current age (the elapsed time since birth) from the father’s current age to get the historical value.

Given Data / Assumptions:

• Daughter now = 10 years.
• Mother now = 3 * 10 = 30 years.
• Father now = Mother + 5 = 35 years.
• “When the daughter was born” means 10 years ago.

Concept / Approach:
Father then = Father now − 10. No ratios after this step; it is a single subtraction using the daughter’s current age as the elapsed time.

Step-by-Step Solution:

Verification / Alternative check:
Ten years ago: Mother 20, Father 25, Daughter 0 (newborn). Today: Mother 30 (still triple the daughter’s 10) and Father 35 (5 years older than mother). Consistent.

Why Other Options Are Wrong:
20/22/30/15 are not equal to Father now (35) minus 10.

Common Pitfalls:
Subtracting 5 (the difference between parents) instead of subtracting the daughter’s age; forgetting that “when born” corresponds to zero age for the child and requires rolling back exactly the child’s current years from everyone’s present ages.

Final Answer:
25 years