In a row of boys, if A who is 10 th from the left and B who is 9 th from the right, interchange their positions, A becomes 15 th from the left. How many boys are there in the row?

Work it out position by position. B is 9th from the right, so with n boys B's position from the left is n − 8. A is 10th from the left before the swap.

After the swap, A moves into B's old spot, which is n − 8 from the left. The question says A is now 15th from the left, so n − 8 = 15, giving n = 23.

• Option A (24): B's spot would be 16th, so A would be 16th, not 15th.
• Option B (31): B's spot would be 23rd, far from 15th.
• Option D (28): B's spot would be 20th, not 15th.

Core concept: a position counted from the left and the same person's position counted from the right always add up to n + 1. Convert every position to one reference point before you solve. This is basic ranking arithmetic and a staple of the reasoning section in the Prelims paper.

Trap: many aspirants take B's position as n − 9 instead of n − 8. That gives n = 24, which is option A, and the question is lost at the first step.