Row at a bus stop – A is 7th from the left; B is 9th from the right. They interchange positions, after which A becomes 11th from the left. How many people are in the row?

Introduction / Context:
Interchange problems hinge on recognizing that after swapping, each person takes the exact former position (from the left) of the other. Use B’s from-right rank to compute the total once you infer B’s former left-position.

Given Data / Assumptions:

• A (before swap): 7th from left.
• B (before swap): 9th from right.
• After swap: A becomes 11th from left → this must equal B’s original left-position.

Concept / Approach:
Let N be total. If B was 9th from right, B’s original left-position is N − 9 + 1 = N − 8. But we’re also told this equals 11 (A’s new position). Solve N − 8 = 11 for N.

Step-by-Step Solution:

Verification / Alternative check:
B’s right-rank from N = 19 is indeed 19 − 11 + 1 = 9. All conditions reconcile.

Why Other Options Are Wrong:
18/20/21 yield inconsistent left/right conversions or violate the post-swap position.

Common Pitfalls:
Forgetting that “becomes 11th from the left” refers to taking the other’s original position; mishandling N − right + 1.

Final Answer:
19