 ## Queues and Ranks

Theory

• This is one of the relatively easier topics because this topic is independent of other topics. Hence, by learning a limited number of concepts, one can score well in questions related to this topic.

• Generally, positions of a few people standing in a queue are given and the candidate is asked to find the total number of people in the group or the position of a certain person with respect to another person.

Formula

• Number of people in the queue = Number of people ahead + 1 person under consideration + number of people behind

• If a person's position is x from start, there are x-1 people ahead of him

• If a person’s position in a queue is x from the front and y from the last, then the total number of people in the queue is x+y-1.

• If a person A’s rank from the front of the queue is x, a person B’s rank from the back of the queue is y, and the number of people in the queue is p, then the number of people between A and B is equal to p-x-y.

Solved Example

In a class of 50 students, Sumit's rank from the top is 15 and Rohit's rank from the bottom is 30. How many people are between Sumit and Rohit?

a) 4
b) 5
c) 6
d) 7
e) None of these

Explanation: Number of people between Sumit and Rohit = 50 - 15 - 30 = 5

Solved Example

If Ravi’s position in the queue is 19th from the front and 23rd from the back, find the number of people in the queue.

A) 40
B) 41
C) 42
D) 43

Solution) We know that if a person’s position in a queue is x from the front and y from the last, then the total number of people in the queue is x+y-1.
Ravi’s position is 19th from the front and 23rd from the back => number of people in the queue = 19 + 23 – 1 = 41 => Answer is B