Ages — three people with ratios to each other and total sum: Raman’s present age is three times his daughter’s and equal to nine-thirteenths of his mother’s. The sum of their present ages is 125 years. Find the difference between the mother’s and daughter’s present ages.

Introduction / Context:Chained ratios allow writing each person’s age in terms of a single variable. A given total then determines exact values.

Given Data / Assumptions:

• Raman = 3 * daughter.
• Raman = (9/13) * mother ⇒ mother = (13/9) * Raman.
• Total (Raman + daughter + mother) = 125.

Concept / Approach:Let daughter = d. Then Raman = 3d; mother = (13/9) * 3d = (13/3)d. Sum and solve for d; compute mother − daughter.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 45, 40 are not equal to the required difference; “Cannot be determined” is incorrect because data are sufficient.

Common Pitfalls:

• Using mother = (9/13) * Raman instead of the inverse.

Final Answer:50 yr