Paresh is 14th from the left and Dileep is 16th from the right in a line of students. When both Paresh and Dileep interchange their positions, the position of Dileep becomes 21st from the right. How many students are there in the line?
34
Understanding the Student Line Position Interchange Problem
This type of reasoning question involves figuring out the total number of individuals in a line when the positions of two people are given both before and after they swap places. The key is to use the information about the changed position to find a person's position from both ends of the line, which then allows you to calculate the total.
Analyzing the Given Information
- Paresh's initial position: 14th from the left.
- Dileep's initial position: 16th from the right.
- Paresh and Dileep interchange positions. This means Paresh is now at Dileep's original spot, and Dileep is now at Paresh's original spot.
- After the interchange, Dileep's new position is 21st from the right.
Finding the Total Number of Students
When Paresh and Dileep interchange their positions, Dileep moves to the spot where Paresh was originally sitting. We know Paresh was 14th from the left. After the swap, Dileep is in this spot, and his position is given as 21st from the right.
This means that the position which is 14th from the left is also 21st from the right.
If we know the position of a single person (or a single spot) from both the left and the right ends of the line, we can find the total number of students using the formula:
Total Students = (Position from Left) + (Position from Right) - 1
In this case, we use the position of the spot where Paresh was originally (and where Dileep is now after the swap):
- Position from Left = Paresh's original position = 14th
- Position from Right = Dileep's new position (at Paresh's original spot) = 21st
Substituting these values into the formula:
Total Students = 14 + 21 - 1
Total Students = 35 - 1
Total Students = 34
Thus, there are 34 students in the line.
Step-by-Step Solution
- Identify the initial positions: Paresh is 14th from the left, Dileep is 16th from the right.
- Understand the interchange: Paresh moves to Dileep's spot, Dileep moves to Paresh's spot.
- Note the new position of one person after the swap: Dileep is now 21st from the right.
- Realize that Dileep's new position is Paresh's original spot.
- Use the information about this spot: it is 14th from the left (Paresh's original position) and 21st from the right (Dileep's new position).
- Apply the formula: Total Students = (Position from Left) + (Position from Right) - 1.
- Calculate: Total Students = 14 + 21 - 1 = 34.
The total number of students in the line is 34.
Revision Table: Key Concepts for Position Interchange
| Concept | Explanation | Application in Problem |
|---|---|---|
| Position from Left/Right | A person's rank counting from one end of the line. | Paresh 14th from left, Dileep 16th from right initially. |
| Position Interchange | Two individuals swap their places in the line. | Paresh takes Dileep's spot, Dileep takes Paresh's spot. |
| New Position after Swap | The rank of a person from an end after swapping places. | Dileep's new position is 21st from the right. |
| Finding Total Students | Using the formula: Pos(Left) + Pos(Right) - 1 for the *same* position. | Using Paresh's original spot (14th from left and 21st from right) to find total students. |
Additional Information: Alternative Method
You can also solve this by first finding how the position change relates to the number of people between them.
- Dileep's original position from the right was 16th.
- Dileep's new position from the right is 21st.
- The difference in Dileep's position from the right is $21 - 16 = 5$.
- This means Dileep moved 5 positions towards the left end of the line.
- The number of people between Paresh and Dileep is the change in position minus 1. So, there are $5 - 1 = 4$ people between Paresh and Dileep.
- Total students can also be calculated as (Paresh's original position from left) + (number of people between them) + (Dileep's original position from right).
- Total Students = 14 (Paresh from left) + 4 (between them) + 16 (Dileep from right) = 34.
- This alternative method confirms the answer obtained using the first method.
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