In a class of 45 students, Rahul is ranked 20th from the top. If the students are arranged in the descending order of ranks, what will be Rahul's position from the bottom?
Understanding Rahul's Rank Calculation
This question asks us to find Rahul's position from the bottom in a class, given his total rank from the top and the total number of students. We need to apply basic ranking logic.
Analyzing the Class Ranking Details
- Total number of students in the class: 45
- Rahul's position from the top: 20th
- Objective: Determine Rahul's position from the bottom.
Key Concepts in Ranking Problems
In any ordered list or ranking, the total number of items is related to the position from the top and the position from the bottom. If you know the total count and one position, you can find the other.
Step-by-Step Calculation for Rank from Bottom
Step 1: Note Down Given Information
We have:
- Total students ($N$) = 45
- Rahul's rank from the top ($R_{top}$) = 20
Step 2: Understand the Relationship Between Ranks
Rahul being 20th from the top means there are 19 students ahead of him (ranked higher). The students ranked below him are the remaining students in the class.
Step 3: Calculate Number of Students Below Rahul
Number of students below Rahul = Total students - Rahul's rank from top
Number of students below Rahul = $N - R_{top}$
$ \text{Number of students below Rahul} = 45 - 20 = 25 $
Step 4: Determine Rahul's Rank from the Bottom
Rahul's rank from the bottom is calculated by adding 1 (for Rahul himself) to the number of students ranked below him.
Rahul's Rank from Bottom ($R_{bottom}$) = (Number of students below Rahul) + 1
$ R_{bottom} = (N - R_{top}) + 1 $
Substituting the values:
$ R_{bottom} = (45 - 20) + 1 $
$ R_{bottom} = 25 + 1 $
$ R_{bottom} = 26 $
Final Position Calculation
Based on the standard calculation, Rahul's position from the bottom is 26th.
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