In a row of boys, Haran is 11th from the left and Manoj is 17th from the right. When they exchange their positions, Haran becomes 13th from the left. What will be Manoj's new position from the right?

Introduction / Context:
This ranking puzzle combines positions from the left and from the right, and introduces an exchange of positions between two boys. After swapping, the rank of one of them is given, and we must determine the new rank of the other from the right. This type of problem tests understanding of how ranks change under position exchanges and how to deduce the total number of persons in the row.

Given Data / Assumptions:

• In the initial arrangement, Haran is 11th from the left.
• In the initial arrangement, Manoj is 17th from the right.
• After they exchange positions, Haran becomes 13th from the left.
• We must find Manoj's new position from the right after the exchange.
• All boys are in a single straight row with fixed total length.

Concept / Approach:
The key idea is that exchanging positions does not change the total number of boys. First use the information after the exchange to calculate the total number of boys in the row. Then use that total to compute Manoj's new position from the right when he stands at Haran's original position. The conversion between ranks from left and right is given by: rank from right = total boys - rank from left + 1.

Step-by-Step Solution:
Step 1: Let the total number of boys be N. Step 2: Initially, Manoj is 17th from the right, so his position from the left is N - 17 + 1 = N - 16. Step 3: After the exchange, Haran takes Manoj's original seat. We are told that Haran then becomes 13th from the left. Step 4: This means N - 16 = 13, because Manoj's original position from the left is now 13 for Haran. Step 5: Solve for N: N - 16 = 13 implies N = 13 + 16 = 29. Step 6: The total number of boys in the row is therefore 29. Step 7: After exchanging positions, Manoj takes Haran's original position, which is 11th from the left. Step 8: Manoj's new position from the right is given by: rank from right = N - rank from left + 1 = 29 - 11 + 1. Step 9: Compute 29 - 11 + 1 = 19. Step 10: Hence Manoj is now 19th from the right.

Verification / Alternative check:
We can do a quick consistency check. With 29 boys, the 13th from the left is 17th from the right because 29 - 13 + 1 = 17. This matches Manoj's original right rank, confirming that Haran's new position after the exchange is indeed Manoj's initial position. Similarly, Manoj at 11th from the left is 29 - 11 + 1 = 19th from the right, confirming our final answer.

Why Other Options Are Wrong:
Options 11 and 13 correspond to left side positions and do not satisfy the right side logic for a total of 29 boys. Option 17 would be the rank from the right for a different left side position and does not align with Haran's original rank or Manoj's new left side rank.

Common Pitfalls:
Some students attempt to guess the total number of boys rather than deducing it algebraically, which can lead to errors. Another common mistake is to forget to include the plus one in conversion formulas, leading to off by one results. Writing the formula carefully and solving step by step avoids these issues.

Final Answer:
After the exchange, Manoj is 19th from the right.