In a row of boys, Punit has position 33rd from the left end and Ankit has position 25th from the right end. After the two boys interchange their positions, Punit becomes 45th from the left end. How many boys are there in the row in total?

Introduction / Context:
This question is about the relationship between left and right positions in a row and how these positions change when two people interchange places. You are given the positions of Punit and Ankit from different ends, before and after they swap places. The goal is to find the total number of boys in the row. These types of problems test understanding of rank formulas and careful handling of position data.

Given Data / Assumptions:
- Initially, Punit is 33rd from the left end. - Initially, Ankit is 25th from the right end. - After they interchange their positions, Punit becomes 45th from the left end. - All boys stand in a single straight row with consecutive positions and no gaps. - We must determine the total number of boys in the row.

Concept / Approach:
The central idea is that when two people swap positions, each takes the other person's original position. After interchange, Punit stands where Ankit originally stood. Therefore, Punit's new left position equals Ankit's original left position. Once we know a boy's position from both ends, we can use the formula total number = left position + right position - 1. We will first calculate Ankit's original position from the left, and then use this formula.

Step-by-Step Solution:
Step 1: Let the total number of boys be N. Step 2: Initially, Ankit is 25th from the right end. Therefore, his position from the left is N - 25 + 1, which simplifies to N - 24. Step 3: After they interchange positions, Punit stands at Ankit's original place. We are told that Punit then becomes 45th from the left. Step 4: Therefore, Ankit's original left position equals 45. So N - 24 = 45. Step 5: Solve for N: N = 45 + 24 = 69. Step 6: Hence, the total number of boys in the row is 69.

Verification / Alternative check:
We can verify by reconstructing positions. If N = 69, Ankit's original left position is 69 - 25 + 1 = 45, which matches the condition that after swapping Punit becomes 45th from the left. Punit's original position from the left is 33, so after swapping Ankit will stand at position 33 from the left. From the right, Ankit's new position would be 69 - 33 + 1 = 37, which does not need to match any given data and creates no contradiction. Therefore, N = 69 is consistent with all information.

Why Other Options Are Wrong:
- If N were 70 or 71, Ankit's original left position would not be 45, so Punit could not become 45th from the left after swapping. - Values such as 68 or 74 similarly fail when we apply the formulas for left and right positions. Only N = 69 satisfies all the given conditions simultaneously.

Common Pitfalls:
Students sometimes forget that after swapping places, each person takes the other's original position. Another common error is misusing the formula for converting right rank to left rank, by forgetting to add or subtract 1. Confusing which boy's position is being referred to after swapping also causes mistakes. Writing down the symbolic expressions carefully and solving step by step helps avoid these issues.

Final Answer:
The total number of boys standing in the row is 69.