In a row Sanjay is at 11 th position from top and 13 th from bottom. How many people are there in the row?
23
Understanding Ranking in a Row Problem
This question involves a common type of ranking or ordering problem. We are given the position of a person, Sanjay, from both ends of a single row. The goal is to find the total number of people present in that row.
When a person's position is given from both the top (or front, or left) and the bottom (or back, or right) in a single line or row, we can determine the total number of individuals in that row using a simple formula.
Calculating Total People in the Row
Let's analyze the information given about Sanjay's position:
- Sanjay is at the 11th position from the top. This means there are 10 people standing before Sanjay (towards the top end).
- Sanjay is at the 13th position from the bottom. This means there are 12 people standing after Sanjay (towards the bottom end).
To find the total number of people in the row, we can add the number of people before Sanjay, Sanjay himself, and the number of people after Sanjay.
- Number of people before Sanjay = Position from top - 1 = $11 - 1 = 10$
- Number of people after Sanjay = Position from bottom - 1 = $13 - 1 = 12$
- Sanjay himself = 1 person
Total people = (People before Sanjay) + (Sanjay) + (People after Sanjay)
Total people = $10 + 1 + 12 = 23$
Using the Ranking Formula
Alternatively, we can use a standard formula for ranking problems where the position of one entity is known from both ends of a linear arrangement.
The formula is:
Total Number of People = (Position from Top) + (Position from Bottom) - 1
The reason we subtract 1 is that when we add the position from the top and the position from the bottom, Sanjay's position is counted twice – once as the 11th person from the top and once as the 13th person from the bottom. To get the unique count of individuals, we must subtract 1 to account for this double counting of Sanjay.
Applying the formula with the given values:
- Position from Top = 11
- Position from Bottom = 13
Total people = $11 + 13 - 1$
Total people = $24 - 1$
Total people = $23$
Both methods yield the same result, confirming that there are 23 people in the row.
Summary of Calculation
| Description | Value |
|---|---|
| Sanjay's position from top | 11th |
| Sanjay's position from bottom | 13th |
| People above Sanjay (11 - 1) | 10 |
| People below Sanjay (13 - 1) | 12 |
| Total people (10 + 1 + 12) | 23 |
| Total people (11 + 13 - 1) | 23 |
Revision Table: Key Ranking Concepts
| Concept | Explanation |
|---|---|
| Ranking | Determining the position of an entity in an ordered sequence. |
| Position from Top/Front/Left | Number of entities before plus the entity itself. |
| Position from Bottom/Back/Right | Number of entities after plus the entity itself. |
| Total in a Row (Formula) | Sum of positions from both ends minus 1 (Total = Pos1 + Pos2 - 1). |
| People Before/After | Position from that end minus 1. |
Additional Information: Variations in Ranking Problems
Ranking problems can have several variations, such as:
- Finding the position from one end if the total and the position from the other end are given.
- Finding the number of people between two individuals.
- Problems involving multiple rows or interchanges of positions.
The core principle for single-row problems with one person's position from both ends remains the formula: Total = Position1 + Position2 - 1. Understanding why we subtract 1 (to correct for double counting) is key to solving these types of ranking questions accurately.
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Important Questions from Ordering and Ranking
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