Row swap using one given side – Jaya is 12th from the left; Rekha is 20th from the right. After swapping, Jaya becomes 22nd from the left. How many students are there?

Introduction / Context:
When a student moves to the other’s seat and we know the new left rank, we can back out the total using the other seat’s original right rank.

Given Data / Assumptions:

• Jaya: 12th from left initially.
• Rekha: 20th from right initially.
• After swapping, Jaya is 22nd from left (so she is at Rekha’s old seat).

Concept / Approach:
Rekha’s old seat had right rank 20 → its left rank is L = N − 20 + 1. After swap, Jaya’s left rank at that seat is 22. Hence N − 20 + 1 = 22.

Step-by-Step Solution:
N − 19 = 22 ⇒ N = 41.

Verification / Alternative check:
In a row of 41, 20th from right maps to 22nd from left (41 − 22 + 1 = 20). Consistent.

Why Other Options Are Wrong:
30/31/34 fail the left/right complement relation implied by the final 22nd position.

Common Pitfalls:
Forgetting the “+1” when converting right rank to left rank.

Final Answer:
41