In a row of boys, A is 10th from the left and B is 9th from the right. After they swap positions, A becomes 15th from the left. How many boys are in the row?

Introduction / Context:When two people swap, each takes the other’s rank from a given side. Use the standard relation between a right-rank and the total size.

Given Data / Assumptions:

• Before swap: A is 10th from left; B is 9th from right.
• After swap: A becomes 15th from left (i.e., A now occupies B’s former seat).

Concept / Approach:If a person is r-th from the right in a row of N, their left-rank is N − r + 1. After swapping, A should have the left-rank that B originally had.

Step-by-Step Solution:

Verification / Alternative check:Check consistency: If N = 23, 9th from right = 15th from left; matches the post-swap rank for A.

Why Other Options Are Wrong:Any other N makes B’s converted left-rank unequal to 15.

Common Pitfalls:Forgetting the +1 when converting between left and right ranks.

Final Answer:23