Time-sequence / positions in a line: In a line of boys, Ganesh is 12th from the left and Rajan is 15th from the right. They interchange their positions. After the swap, Rajan is 20th from the right. Find the total number of boys in the class.

Introduction / Context:
This rank/position puzzle asks you to convert left/right positions to a single total using the identity: position_from_right = N - position_from_left + 1. Swapping helps us anchor N.

Given Data / Assumptions:

• Ganesh: 12th from left (before swap).
• Rajan: 15th from right (before swap).
• After swapping, Rajan sits where Ganesh was and is 20th from right.

Concept / Approach:
For any fixed seat, its “from right” position equals N - (from left) + 1. Use the seat that was 12th from left (Ganesh’s original seat) because Rajan occupies it after swapping and we are told his right-rank there.

Step-by-Step Solution:

Verification / Alternative check:
If N = 31, then a seat 12th from left is (31 - 11) = 20th from right, matching the post-swap statement. Consistent.

Why Other Options Are Wrong:
Any N ≠ 31 gives a different right-rank for the 12th-from-left seat, contradicting the given “20th from right.”

Common Pitfalls:
Forgetting the +1 in the conversion formula, or trying to use both students’ original positions simultaneously (unnecessary here).

Final Answer:
31