In a row A is in the 11th position from the left and B is in the 10th position…

Concept. In a single straight row, a person who stands at place p counted from the left and at place q counted from the right is counted once from each end, while occupying only one place. That one shared place is counted twice, so the strength of the whole row is p + q − 1. Once the row strength is known, the number of people standing in it apart from any two named individuals is that strength reduced by 2.

Application to this row.

1. A and B exchange places with each other, so after the exchange A is standing in exactly the place B occupied before it.

2. After the exchange A is 18th from the left, so the place B originally occupied was the 18th place from the left.

3. B is also given as 10th from the right, so B stands 18th from the left and 10th from the right at the same time.

4. Applying the rule with p = 18 and q = 10, the strength of the row is 18 + 10 − 1 = 27.

5. The question asks for the people other than A and B, so remove those two individuals from the strength: 27 − 2 = 25.

Cross-check. In a row of 27 people the person standing 10th from the right stands at place 27 − 10 + 1 = 18 from the left, which is exactly the place A reaches after the exchange, so the strength 27 is consistent with both statements. A’s own starting place, 11th from the left, is not needed to obtain the count; it only establishes that A and B stood at different places before the exchange. The row therefore contains 25 people besides A and B.