Row in East–West direction – swap positions and count total: Dipika is 11th from the West. Sudesh is 15th from the East. After exchanging positions, Sudesh becomes 9th from the East. How many persons are in the row?

Introduction / Context:
When two people swap seats, each takes the other’s rank. Using this fact with left/right conversions yields the total number of persons in the row.

Given Data / Assumptions:

• Dipika = 11th from West.
• Sudesh = 15th from East (before swap).
• After swap, Sudesh is 9th from East.

Concept / Approach:
After exchanging positions, Sudesh acquires Dipika’s original seat. Let N be total persons. The left-rank of Dipika’s seat is 11; the equivalent right-rank is N − 11 + 1 = N − 10. This must equal Sudesh’s new right-rank 9.

Step-by-Step Solution:

Verification / Alternative check:
With N = 19, the position 11 from West corresponds to 9 from East (19 − 11 + 1 = 9), matching the given post-swap status of Sudesh.

Why Other Options Are Wrong:
All other totals produce a different right-rank than 9 after the swap.

Common Pitfalls:
Missing the +1 in conversions or mistakenly swapping the wrong ranks.

Final Answer:
19