Row swap & total – Dilip is 10th from the left; Jagdish is 20th from the right. They swap places and Jagdish becomes 23rd from the right. How many students are in the row?

Introduction / Context:
When a person’s position is known from one side after a swap, combine left and right ranks for that same final position to compute total N via N = L + R − 1.

Given Data / Assumptions:

• Dilip (before swap): 10th from left.
• Jagdish (before swap): 20th from right.
• After swapping, Jagdish is at Dilip’s old seat and is 23rd from right.

Concept / Approach:
After swap, Jagdish’s left rank equals Dilip’s original left rank (=10). Combine with his new right rank (=23).

Step-by-Step Solution:
N = left + right − 1 = 10 + 23 − 1 = 32.

Verification / Alternative check:
Check complements: In a row of 32, 10th from left corresponds to 23rd from right (since 32 − 10 + 1 = 23). Consistent.

Why Other Options Are Wrong:
33/42/44 violate the complement formula for the observed final ranks.

Common Pitfalls:
Using Jagdish’s original right rank (20) instead of his final right rank (23) in the formula.

Final Answer:
32