Queue Positions

Algebra Level 1

Some students, including Rohit and Pranshu, are standing in a queue.

  • Rohit is standing at the 4 th 4^\text{th} position from the back of the queue.
  • Pranshu is standing at the 5 th 5^\text{th} position from the front of the queue.
  • If they switched places, then Pranshu would be standing at the 9 th 9^\text{th} position from the front of the queue.

How many students are standing in the queue?


The answer is 12.

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3 solutions

Chew-Seong Cheong
Dec 23, 2017

Let the number of students standing in the queue be n n . Then the position Rohit was originally standing, the 4th from the last is number ( n 3 ) (n-3) th from the front. He switched positions with Pranshu, but the position is still remained as ( n 3 ) (n-3) th from the front, which is 9th. Therefore, n 3 = 9 n-3=9 , n = 12 \implies n = \boxed{12} .

Aaryan Vaishya
Dec 27, 2018

The 1st and 3rd statements indicate that Rohit is 4th from the back and 9th from the front.We add 4 and 9=13 and subtract 1 because we counted Rohit twice.

Bibhor Singh
Dec 23, 2017

It can be solved by drawing a fictional line.

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