Mother–daughter age relation with past multiple: A mother is 25 years older than her daughter. Five years ago, the mother’s age was 6 times the daughter’s age. What is the mother’s current age?

Introduction / Context:
The mix of a fixed present difference and a past multiplicative relationship yields a single linear equation. Solve using a present variable and a time shift to the past.

Given Data / Assumptions:

• Daughter now = x; Mother now = x + 25.
• Five years ago: mother = 6 × daughter.

Concept / Approach:
Set (x + 25 − 5) = 6(x − 5) and solve for x; then compute the mother’s current age.

Step-by-Step Solution:
1) x + 20 = 6x − 30.2) 50 = 5x ⇒ x = 10.3) Mother now = x + 25 = 35 years.

Verification / Alternative check:
Five years ago: daughter = 5, mother = 30; indeed, 30 = 6 × 5. The data are consistent.

Why Other Options Are Wrong:

• 25/29/32/40 do not satisfy the 6× condition when checked backwards with a present difference of 25.

Common Pitfalls:
Forgetting to subtract 5 from both ages or mixing up whose age is a multiple of whose can lead to errors.

Final Answer:
35 years