In a row, Kumar is at seventh place from the left end and Pawan is at ninth place from the right end. After they interchange their positions, Kumar becomes eleventh from the left. How many persons are seated in the row?

Introduction / Context:
Here you are given a typical ranking puzzle where two people in a row interchange their positions. You know their positions from different ends before and after the interchange. The problem tests your understanding of how to convert between left and right ranks and how to use that information to determine the total number of persons in the row.

Given Data / Assumptions:
- Kumar is seventh from the left before interchange. - Pawan is ninth from the right before interchange. - After interchange, Kumar becomes eleventh from the left. - The total number of persons in the row is fixed and is to be found.

Concept / Approach:
The main idea is that after interchange, each person occupies the other person's original position. So, when Kumar becomes eleventh from the left after the swap, he is now occupying the position that originally belonged to Pawan. That means Pawan's original position from the left must be the eleventh place. Using the relationship between left and right ranks in a row of N persons, we can form an equation to solve for N.

Step-by-Step Solution:
Step 1: Let N be the total number of persons in the row. Step 2: Before interchange, Kumar is seventh from the left, so his original left rank is 7. Step 3: Before interchange, Pawan is ninth from the right. His original position from the left is N - 9 + 1 = N - 8. Step 4: After they swap, Kumar takes Pawan's original position. According to the question, Kumar is now eleventh from the left. Step 5: Therefore Pawan's original position from the left, N - 8, must equal 11. Step 6: Set up and solve the equation: N - 8 = 11. Step 7: From this, N = 11 + 8 = 19. Step 8: Hence there are 19 persons seated in the row.

Verification / Alternative check:
Check consistency by computing Pawan's new position after the swap. Originally Kumar was seventh from the left. In a row of 19 persons, the seventh position from the left corresponds to right rank = N - 7 + 1 = 19 - 7 + 1 = 13. So, after swap, Pawan becomes thirteenth from the right. This is consistent and does not contradict any given information. Also, Pawan's original left rank N - 8 indeed becomes 11 when N equals 19, verifying the equation.

Why Other Options Are Wrong:
20: If N were 20, Pawan's original left position would be 20 - 8 = 12, not 11. 21: For N = 21, Pawan's left position would be 13, which again does not match eleven. 27: This is far from the correct row size and produces an inconsistent left position for Pawan.

Common Pitfalls:
Many learners confuse whose position is being described after interchange and mistakenly apply the formula to the wrong person. Others incorrectly set the relationship N - 9 instead of N - 9 + 1, forgetting to add one. Carefully labeling original and new positions for each person and writing a clear equation avoids these misunderstandings in ranking problems.

Final Answer:
The total number of persons seated in the row is 19.