Question

Aruna and Sudeshana are standing in a queue. Aruna is 5th from the front and Sudeshana is 6th from the end. Now, they interchange their position. Now, Aruna is 13th from the front. Find the position of Sudeshana from the end after the interchange.

• A. 18th
• B. 15th
• C. 14th
• D. Cannot be determined

Hint:

When people interchange positions in a queue, calculate the total number of people and then find their new positions based on the given information.

Answer 1

The Correct Option is C

Let the total number of people in the queue be \( n \). Step 1: Position of Aruna and Sudeshana before interchange.
Aruna is 5th from the front, so her position is 5. Sudeshana is 6th from the end, so her position from the front is \( n - 6 + 1 = n - 5 \). Step 2: Position after interchange.
After the interchange, Aruna is 13th from the front. So, her new position is 13. The position of Sudeshana from the front is now 5 (since Aruna and Sudeshana exchanged places). Step 3: Find the total number of people.
We know that Aruna's new position is 13th. Sudeshana's new position is 5th. The total number of people can be found by equating Sudeshana's new position and Aruna's original position: \[ n - 5 = 13 \] Thus, \[ n = 18 \] Step 4: Sudeshana's position from the end.
The position of Sudeshana from the end is: \[ \text{Position from the end} = n - 5 + 1 = 18 - 5 + 1 = 14 \] Thus, the position of Sudeshana from the end after the interchange is 14th. Final Answer: \[ \boxed{14th} \]