Queue Position Calculation Explained
This question involves finding the total number of people in a line (queue) given an individual's position from both the front and the back of the line. We need to determine the total count based on the provided information about Ram's position.
Understanding the Problem
We are given the following information:
- Ram's position from the front of the queue is \(10^{th}\).
- Ram's position from the back of the queue is \(15^{th}\).
Our goal is to find the total number of people in the queue.
Formula for Total People in a Queue
When you know the position of a person from both ends (front and back), you can calculate the total number of people in the queue using the following formula:
\(Total People = (Position from Front) + (Position from Back) - 1\)
We subtract 1 because the person (Ram, in this case) is counted twice – once from the front and once from the back. By subtracting 1, we ensure Ram is counted only once.
Step-by-Step Calculation
Let's apply the formula using the given values:
- Position from Front: Ram is the \(10^{th}\) person from the front.
- Position from Back: Ram is the \(15^{th}\) person from the back.
- Calculate Total:
- Add the two positions: \(10 + 15 = 25\).
- Subtract 1 to correct for double counting Ram: \(25 - 1 = 24\).
So, the calculation is:
\(Total People = 10 + 15 - 1\)
\(Total People = 25 - 1\)
\(Total People = 24\)
Conclusion
There are 24 people in the queue. Ram is the \(10^{th}\) person from the front, meaning there are 9 people in front of him. He is the \(15^{th}\) person from the back, meaning there are 14 people behind him. The total count is \(9 (\text{in front}) + 1 (\text{Ram}) + 14 (\text{behind}) = 24\).
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