Two-person age gap and a past double: The age difference between two persons is 10 years. Fifteen years ago, the elder was twice the younger. What is the elder’s present age?

Introduction / Context:
This is a linear age system deriving from a fixed difference and a multiplicative past relation. Assign the younger's age as a variable, express the elder as “younger + 10,” then apply the past relation to solve quickly.

Given Data / Assumptions:

• Let younger be y; elder is y + 10 now.
• 15 years ago: (y + 10 − 15) = 2(y − 15).
• Ages are positive and consistent with the past constraint.

Concept / Approach:
Set up the single linear equation in y and solve. Restore the elder’s current age by adding the 10-year difference back to the solution for y.

Step-by-Step Solution:

Verification / Alternative check:
Fifteen years ago: elder 20, younger 10 → indeed 20 = 2 × 10.

Why Other Options Are Wrong:
25/45/55 do not satisfy the doubled condition 15 years ago together with the 10-year gap.

Common Pitfalls:
Applying the 15-year subtraction to only one person; both are 15 years younger in the past.

Final Answer:
35 years