Ages ratio puzzle — ten years ago, the ratio of A's age to B's age was 13:17. Seventeen years from now, the ratio of their ages will be 10:11. What is B's present age?

Introduction / Context:
Age-ratio questions test the ability to translate statements about the past and future into present-age equations. The key is to set present ages as variables and then apply given ratios at different times consistently.

Given Data / Assumptions:

• 10 years ago: A : B = 13 : 17
• 17 years from now: A : B = 10 : 11
• All ages are in years and are positive integers.

Concept / Approach:
Let present ages be A = a and B = b. Convert each ratio statement into a linear equation using cross-multiplication. Solve the two linear equations to get a and b.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 23 yr: That is A's present age, not B's.
• 40 yr and 44 yr: These are future ages, not present ages.
• None of these: Incorrect because 27 yr matches B exactly.

Common Pitfalls:
Mixing up which ratio applies to which time; forgetting to adjust both ages by the same number of years; or solving only one equation. Always form two equations and solve simultaneously.

Final Answer:
27 yr