Row positions after swapping: In a row of boys, Rajan is 10th from the right and Suraj is 10th from the left. After Rajan and Suraj interchange their positions, Suraj becomes 27th from the left. What is Rajan's position from the right after the swap?

Introduction / Context:This is a classic rank-and-position problem. You relate “from left” and “from right” positions via the total count, then apply a swap to infer the new ranks. The trick is to deduce the total number of boys first.

Given Data / Assumptions:

• Rajan is 10th from the right initially.
• Suraj is 10th from the left initially.
• After swapping places, Suraj becomes 27th from the left.

Concept / Approach:For a line of length n, if a person is r-th from the right, their rank from left is n - r + 1. Swapping exchanges seats (positions), so post-swap ranks equal the partner’s original seat coordinates.

Step-by-Step Solution:

Verification / Alternative check:List left ranks for both initially: Suraj 10th; Rajan (from left) = 27th. Swap them: they simply exchange these left ranks (10 ↔ 27). Then convert Rajan’s new left rank (10) into right rank: 27. Consistent.

Why Other Options Are Wrong:

• 26th/25th/29th/10th: Do not match the computed n = 36 and the conversion formula.

Common Pitfalls:Forgetting the +1 in the conversion (n - left + 1 or n - right + 1), or assuming n = 35 by mistake.

Final Answer:27th