Two-time ratios to present ages: Seven years ago, A : B = 3 : 4. Nine years hence, A : B = 7 : 8. What is B’s present age?

Introduction / Context:
Again, two ratios at different times produce a solvable linear system for present ages. Translate carefully and solve systematically to avoid arithmetic slips.

Given Data / Assumptions:

• (A − 7) : (B − 7) = 3 : 4
• (A + 9) : (B + 9) = 7 : 8

Concept / Approach:
Cross-multiply each, reduce to standard linear form, and solve by elimination or substitution.

Step-by-Step Solution:

Verification / Alternative check:
Seven years ago: 12 : 16 = 3 : 4; in nine years: 28 : 32 = 7 : 8 ✓.

Why Other Options Are Wrong:
16, 19, 28 are not B’s present age under the constraints; only 23 fits.

Common Pitfalls:
Arithmetic slips when distributing and moving constants; ensure both persons’ ages shift by the same amount in each time frame.

Final Answer:
23 yr