All 32 students in a class are standing in a row facing north. Akash is 12th from the right end while Priya is 18th from the left end. How many people are standing between Akash and Priya?
Two
Understanding the Ranking Problem
This problem involves understanding positions in a linear arrangement, also known as a ranking or row arrangement problem. We are given the total number of students in a row and the positions of two students, Akash and Priya, from opposite ends. Our goal is to find the number of students standing between them.
Analysing Given Positions
We have the following information:
- Total number of students in the row: 32
- Akash's position from the right end: 12th
- Priya's position from the left end: 18th
To find the number of people between Akash and Priya, we first need to know their positions from the same end. Let's convert their positions to be from the left end.
Calculating Positions from the Opposite End
If a person's position from one end is known, their position from the other end can be calculated using the formula:
Position from other end = (Total number of people) - (Position from the given end) + 1
Akash's Position from the Left End
Akash is 12th from the right end. Total students are 32.
Akash's position from the left end = $32 - 12 + 1$
Akash's position from the left end = $20 + 1 = 21$st
So, Akash is 21st from the left end.
Priya's Position from the Left End (Already Given)
Priya's position from the left end is already given as 18th.
Finding the Number of Students Between Akash and Priya
Now we know both Akash's and Priya's positions from the left end:
- Priya is 18th from the left.
- Akash is 21st from the left.
Since Akash is further from the left end (21st) than Priya (18th), Akash is to the right of Priya in the row. The students between them are those who are after Priya (from the left) and before Akash (from the left).
Their positions from the left end are 18, 19, 20, 21, ...
Priya is at position 18.
Akash is at position 21.
The students between them are at positions 19 and 20 from the left end.
To find the number of students between two people when their positions from the same end are known, we can use the formula:
Number of people between = |Position of one person - Position of other person| - 1
Using their positions from the left end:
Number of people between = $|21 - 18| - 1$
Number of people between = $|3| - 1$
Number of people between = $3 - 1 = 2$
There are 2 students standing between Akash and Priya.
Summary of Positions
| Student | Position from Left | Position from Right |
|---|---|---|
| Priya | 18th | $32 - 18 + 1 = 15$th |
| Akash | $32 - 12 + 1 = 21$st | 12th |
From the table, we can see Akash (21st from left, 12th from right) and Priya (18th from left, 15th from right). They are on different sides of the exact middle of the row. Priya is at 18 from the left, Akash is at 21 from the left. People between them are at 19 and 20. That's 2 people.
Conclusion
By converting Akash's position to be from the left end, we found that he is 21st from the left. Since Priya is 18th from the left, and Akash is 21st from the left, there are students at positions 19 and 20 between them. Thus, there are 2 students between Akash and Priya.
Revision Table: Ranking and Row Arrangement
| Concept | Description | Formula/Example |
|---|---|---|
| Total in a Row | Sum of positions from left & right minus 1. | Total = Left Rank + Right Rank - 1 |
| Rank from Opposite End | Calculating position from the other end of the row. | Opposite Rank = Total - Given Rank + 1 |
| People Between (Same End) | Number of individuals between two people when their ranks from the same end are known. | Between = |Rank1 - Rank2| - 1 |
| People Between (Opposite End & No Overlap) | Number of individuals between two people when their ranks from opposite ends are known and Total >= Rank1 + Rank2. | Between = Total - (Rank1 + Rank2) |
| People Between (Opposite End & Overlap) | Number of individuals between two people when their ranks from opposite ends are known and Total < Rank1 + Rank2 (indicates overlap). | Between = (Rank1 + Rank2) - Total - 2 |
Additional Information: Types of Ranking Problems
Ranking and row arrangement problems in logical reasoning can involve various scenarios:
- Finding the total number of people in a row.
- Finding a person's rank from the opposite end.
- Finding the number of people standing between two individuals.
- Finding a person's rank based on their relative position to another person.
- Finding the total number of people or a person's rank after an interchange of positions.
Understanding how to calculate positions from both ends and the formulas for finding people between is crucial for solving these types of questions accurately.
Important Questions from Rank Based
In a class of 36 students, the number of boys are twice the number of girls. In the class, there are 13 boys before Reema (girl) whose position is 19th in the class. How many girls are there in the class after Reema?
In a row of 21 children facing North, Nitin is third to the right of Sita who is ninth from the right end of the row. What is Nitin's position from the left end?
Selvam is on 9th position from upwards and on 38th position from downwards in a class. How many students are in class?
Six students, Abhay, Bhanu, Charu, David, Ekta and Farheen, are the top six rank holders in a school. The rank of Bhanu is between the ranks of Charu and David. Bhanu is on the fourth rank. There are two students between the ranks of Ekta and David. Ekta is at the lowest rank among all the given students. The rank of Abhay is immediately below the rank of Farheen. Who is on the fifth rank?
In a row of 35 students, Ramesh is at the 24th position from the beginning. The last two students left. What is Ramesh's position from the end of the row?
