Shahid and Purnima are standing in queue for a railway ticket. Shahid is the 7 th from the counter and the 27 th from the end. Purnima is the 12th from the end. How many people are ahead of her?
21
Understanding the Queue Ranking Problem
This question involves a common type of ranking or position problem where we need to determine the total number of people in a queue and then figure out someone's position relative to others.
Calculating Total Number of People in the Queue
We are given information about Shahid's position from both the front (counter) and the back (end) of the queue. This allows us to find the total number of people.
If a person is at position \(P_f\) from the front and \(P_b\) from the back in a queue, the total number of people (\(N\)) in the queue can be calculated using the formula:
\( N = P_f + P_b - 1 \)
In Shahid's case:
- Shahid's position from the front (\(P_f\)) = 7th
- Shahid's position from the back (\(P_b\)) = 27th
Using the formula, the total number of people is:
\( N = 7 + 27 - 1 \)
\( N = 34 - 1 \)
\( N = 33 \)
So, there are a total of 33 people in the railway ticket queue.
Finding Purnima's Position from the Front
We know the total number of people in the queue (33) and Purnima's position from the back (end).
- Purnima's position from the back (\(P_b\)) = 12th
- Total number of people (\(N\)) = 33
To find Purnima's position from the front (\(P_f\)), we can rearrange the total number formula:
\( N = P_f + P_b - 1 \)
\( P_f = N - P_b + 1 \)
Substituting the values for Purnima:
\( P_f = 33 - 12 + 1 \)
\( P_f = 21 + 1 \)
\( P_f = 22 \)
Purnima is the 22nd person from the front of the queue.
Determining People Ahead of Purnima
The question asks how many people are ahead of Purnima. If Purnima is the 22nd person from the front, it means there are 21 people standing before her in the queue.
Number of people ahead of Purnima = Purnima's position from the front - 1
Number of people ahead = \( 22 - 1 \)
Number of people ahead = \( 21 \)
Therefore, there are 21 people ahead of Purnima in the queue.
Important Questions from Rank Based
In a row of forty children, R is eleventh from the right end and there are fifteen children between R and M. What is M’s position from the left end of the row?
Keerthi ranked 17 th from the top in a class of thirty-one students. What is his rank from the bottom?
Price of five cars A, L, J, M and T are compared. Price of A is the least. No two cars have the same price. Price of J is less than T. L and M. Price of neither T nor L is the highest. Price of T is less than L. Price of how many cars is more than the price of T?
200 people are sitting in a row. Asha is in the 20th place from the left and Anna is in the 31st position from the right. How many people are sitting between them?
In a queue, A stands 14th from the front and B 17th from the last. C is exactly at the middle of the queue with 16 persons between him and A. How many persons are between B and C?
