Swap positions in a line — deduce total and new index In a line of students, Madhukar is 15th from the right and Dhirendra is 18th from the left. After they interchange positions, Madhukar is 20th from the right. What is Dhirendra’s position from the left?

Introduction / Context:Interchanging positions swaps exact seats. Use the conversion L = N − R + 1 to determine N first, then the resulting index.

Step-by-Step Solution:After swap, Madhukar's right-rank equals Dhirendra's original right-rank.Dhirendra original right-rank = N − 18 + 1 = N − 17.Given after swap Madhukar is 20th from right ⇒ N − 17 = 20 ⇒ N = 37.Dhirendra's new left-rank equals Madhukar's original left-rank: N − 15 + 1 = 23.

Verification / Alternative check:Sum checks: original (Madhukar) 15th from right ⇒ left = 37 − 15 + 1 = 23; consistent with the result required.

Final Answer:23rd