In a row of boys, Punit occupies the 33rd position from the left end and Ankit occupies the 25th position from the right end. After they interchange their positions in the same row, Punit is now 45th from the left. Based on this information, how many boys are there in the row in total?

Introduction / Context: This problem is a standard example of rank and order reasoning. Two boys exchange positions in a row, and you must determine the total number of boys. The key idea is to use the relationship between rank from the left, rank from the right and the total number of boys in the line. Given Data / Assumptions:

• Before interchange, Punit is 33rd from the left end.
• Before interchange, Ankit is 25th from the right end.
• After interchange, Punit becomes 45th from the left end.
• All boys remain in a single straight row, and no one leaves or joins the row.

Concept / Approach: If there are N boys:

• Rank from right = N - (rank from left) + 1.
• When two boys interchange positions, each takes the other's original position.

We will express the positions of Punit and Ankit in terms of N and then use the new rank after interchange to find N. Step-by-Step Solution: Step 1: Let total number of boys be N. Step 2: Initially, Punit is 33rd from the left; his position from the right would be N - 33 + 1 = N - 32. Step 3: Initially, Ankit is 25th from the right; his position from the left is N - 25 + 1 = N - 24. Step 4: When they interchange positions, Punit takes Ankit's former place. So, after interchange, Punit should be at position N - 24 from the left. Step 5: The question tells us that, after interchange, Punit is actually 45th from the left. Step 6: Therefore, we equate N - 24 = 45. Step 7: Solve for N: N = 45 + 24 = 69. Step 8: Hence, there are 69 boys in the row. Verification / Alternative check: We can verify by computing Ankit's new rank. Before interchange, Ankit was N - 24 from left, which is 69 - 24 = 45. After interchange, Ankit goes to Punit's old position, which is 33rd from the left. From the right, this becomes 69 - 33 + 1 = 37. All positions are consistent, confirming N = 69. Why Other Options Are Wrong: 70, 71, 74, 68: Each of these alternatives would break the equality N - 24 = 45 or would make the new ranks inconsistent. For example, if N were 70, then N - 24 = 46, which does not equal the given final rank 45 from the left. Common Pitfalls: A common mistake is to mix up which position is being swapped. Remember that after the interchange, each boy takes the other's original seat. Another frequent error is forgetting to add 1 when converting ranks from the right to ranks from the left or vice versa, which leads to off-by-one errors and wrong totals. Final Answer: The total number of boys standing in the row is 69.