Queue Positions

Algebra Level 1

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

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

How many students are standing in the queue?

The answer is 12.

3 solutions

Chew-Seong Cheong
Dec 23, 2017

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

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.

Queue Positions

The answer is 12.

3 solutions

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