Recover present ages from ratio and past difference: Ramesh : Jayesh = 3 : 2 (present). Four years ago, Ramesh was 6 years older than Jayesh. Find Jayesh’s present age.

Introduction / Context:Combine a present-time ratio with a past-time difference. Express both present ages by a common factor and use the past condition to solve for the factor.

Given Data / Assumptions:

• R : J = 3 : 2 ⇒ R = 3k, J = 2k
• Four years ago, R − 4 = (J − 4) + 6

Concept / Approach:Translate the past statement into an equation in k and solve. Then compute the requested present age of Jayesh.

Step-by-Step Solution:

Verification / Alternative check:Four years ago: R = 18−4=14, J = 12−4=8; difference = 6 ✓.

Why Other Options Are Wrong:18 and 6 don’t satisfy both constraints together; “Data is inadequate” is false because the system is solvable and determinate.

Common Pitfalls:Forgetting to apply the 4-year subtraction to both ages in the past condition; mixing present and past variables.

Final Answer:12 years