After 10 years, A will be twice as old as B was 10 years ago. If A is currently 9 years older than B, what is B's present age?

Introduction / Context:This problem mixes a future age with a past age and adds a present-age difference. Carefully track times for both people and set up precise equations.

Given Data / Assumptions:

• Let present ages be A and B.
• After 10 years: A + 10 = 2(B − 10)
• Now: A = B + 9

Concept / Approach:Substitute A = B + 9 into the future–past relation to produce a single linear equation in B. Solve for B, then verify with both statements.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 19, 29, 49 do not satisfy both constraints.
• None of these is unnecessary since 39 works.

Common Pitfalls:Using A + 10 = 2(B + 10) (wrong time reference for B); or mistakenly setting A − B = 9 after shifting the timeline rather than at present only.

Final Answer:39 years