Calculating Rank from the Bottom in a Class

This problem involves determining a student's rank from the bottom of a list when their rank from the top and the total number of students are known. These types of ranking problems are common in aptitude and reasoning sections of competitive exams.

Understanding the Ranking Concept

When students are ranked in a list, each student occupies a unique position. The rank from the top counts positions starting from the first student, while the rank from the bottom counts positions starting from the last student.

Consider a simple example: If there are 5 students (A, B, C, D, E) ranked from top to bottom.

• Student A is 1st from the top.
• Student B is 2nd from the top.
• Student C is 3rd from the top.
• Student D is 4th from the top.
• Student E is 5th from the top.

Now, let's look at the rank from the bottom:

• Student E is 1st from the bottom.
• Student D is 2nd from the bottom.
• Student C is 3rd from the bottom.
• Student B is 4th from the bottom.
• Student A is 5th from the bottom.

Notice that for any student, say Student C, their rank from the top is 3 and their rank from the bottom is 3. The total number of students is 5. If we add their rank from the top and rank from the bottom (3 + 3 = 6), it's one more than the total number of students (5). This is because the student's position is counted twice (once from the top and once from the bottom).

Formula for Ranking Problems

The relationship between the total number of students, the rank from the top, and the rank from the bottom is given by the formula:

\( \text{Total number of students} = \text{Rank from top} + \text{Rank from bottom} - 1 \)

To find the rank from the bottom, we can rearrange this formula:

\( \text{Rank from bottom} = \text{Total number of students} - \text{Rank from top} + 1 \)

Similarly, to find the rank from the top:

\( \text{Rank from top} = \text{Total number of students} - \text{Rank from bottom} + 1 \)

Applying the Formula to Rohit's Rank

In this question, we are given:

• Total number of students in the class = 40
• Rohit's rank from the top = 17

We need to find Rohit's rank from the bottom.

Using the formula:

\( \text{Rank from bottom} = \text{Total number of students} - \text{Rank from top} + 1 \)

Substitute the given values:

\( \text{Rohit's rank from bottom} = 40 - 17 + 1 \)

First, calculate the difference:

\( 40 - 17 = 23 \)

Then, add 1:

\( 23 + 1 = 24 \)

Therefore, Rohit's rank from the bottom is 24.

Step-by-Step Calculation Summary

1. Identify the total number of students: 40.
2. Identify the given rank (from the top): 17.
3. Use the formula: Rank from bottom = Total students - Rank from top + 1.
4. Substitute the values: \( 40 - 17 + 1 \).
5. Calculate: \( 23 + 1 = 24 \).

Rohit ranks 24th from the bottom in the class.

Revision Table: Ranking Concepts

Additional Information: Ranking Problems

Ranking problems often appear in logical reasoning and quantitative aptitude tests. They can involve a single person's position, the positions of two people relative to each other, or finding the number of people between two individuals. Key things to remember:

• The total number of items/students is always one less than the sum of ranks from opposite ends because one person's position is counted twice.
• Carefully read if the rank is from the top, bottom, left, or right. The principle remains the same.
• Sometimes, questions might involve multiple people, and you might need to find the number of people between them based on their ranks. This can be done by finding the difference in ranks and subtracting one.
• Practice with different variations of ranking problems helps build confidence and speed for exams.