Sunil is 40 years old and Anil is 60 years old today. How many years ago was the ratio of their ages 3:5?

Introduction / Context:This is a standard back-dating age ratio problem. We translate “x years ago” into (present age − x) and impose the ratio.

Given Data / Assumptions:

• Present ages: Sunil = 40, Anil = 60
• We seek x such that (40 − x) : (60 − x) = 3 : 5

Concept / Approach:Use the ratio definition and cross-multiply to form a linear equation in x. Solve for x and ensure it is feasible (nonnegative and less than both present ages).

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 5, 12, 15 years: Substituting these values will not yield the ratio 3:5.
• None of these: We have a valid solution at 10 years.

Common Pitfalls:Setting (older − x)/(younger − x) to the inverse ratio; or forgetting that the same x is subtracted from both ages in the past scenario.

Final Answer:10 years