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Difficulty: HardOrder and Ranking

In a straight row of cadets facing North, Vikram is positioned 13th13^{\text{th}} from the left end and Rahul is positioned 31st31^{\text{st}} from the right end. If they interchange their positions, Vikram becomes 39th39^{\text{th}} from the left end. Another cadet, Sanjay, is standing exactly in the middle of Vikram and Rahul's new positions. What is Sanjay's position from the right end?

  1. 44th44^{\text{th}}Answer
  2. B
    26th26^{\text{th}}
  3. C
    43rd43^{\text{rd}}
  4. D
    45th45^{\text{th}}

Answer

Sanjay's position is 44th44^{\text{th}} from the right end.
The correct answer accurately determines the total number of cadets as 6969 by combining the left and right ranks of the intersection seat. It identifies Sanjay's position as 26th26^{\text{th}} from the left by averaging 1313 and 3939, and finally correctly converts this to the 44th44^{\text{th}} position from the right using the formula N−L+1N - L + 1.

Step-by-Step Solution

1
Calculate the total number of cadets in the row.
Total = 39+31−1=6939 + 31 - 1 = 69 cadets.
After the swap, Vikram is 39th39^{\text{th}} from the left. This physical seat is the same as Rahul's original seat, which was 31st31^{\text{st}} from the right. The formula for total is L+R−1L + R - 1.
2
Determine the new positions of Vikram and Rahul from the left end.
Vikram's new position = 39th39^{\text{th}} from the left. Rahul's new position = 13th13^{\text{th}} from the left.
Since they swapped, Rahul occupies Vikram's original seat, which is 13th13^{\text{th}} from the left.
3
Calculate Sanjay's position from the left end.
Sanjay's position = (13+39)÷2=26th(13 + 39) \div 2 = 26^{\text{th}} from the left.
Sanjay is exactly in the middle of 1313 and 3939, so we average the two positions.
4
Convert Sanjay's position from the left end to the right end.
Sanjay's position from the right = 69−26+1=44th69 - 26 + 1 = 44^{\text{th}}.
The formula to find the rank from the opposite end is Total−Current Rank+1\text{Total} - \text{Current Rank} + 1.

Key Concept

Position Interchange and Midpoint Calculations
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Topics

Order and Ranking

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