Understanding Student Rank from Top and Bottom

This question asks us to find a student's rank from the bottom of a class given their rank from the top and the total number of students in the class. This is a common type of ranking problem.

Let's break down the information given:

• Total number of students in the class = 30
• Aaditya's rank from the top (merit order) = 11^th

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

Calculating Rank from Bottom

To find the rank from the bottom, we can use a simple formula. Consider the students ranked from 1 to 30. If Aaditya is at the 11^th position from the top, it means there are 10 students above him.

The total number of students is 30. If Aaditya is at 11^th place from the top, the number of students below him is the total number of students minus his rank from the top.

Number of students below Aaditya = Total students - Aaditya's rank from top

Number of students below Aaditya = $30 - 11 = 19$ students.

If there are 19 students below Aaditya, his rank from the bottom will be one more than the number of students below him (because we are counting his position as well).

Aaditya's rank from bottom = Number of students below Aaditya + 1

Aaditya's rank from bottom = $19 + 1 = 20$.

So, Aaditya's rank from the bottom is 20^th.

Alternative Formula for Ranking Problems

A more direct formula to calculate the rank from the other end is:

Rank from bottom = Total number of students - Rank from top + 1

Let's apply this formula:

Rank from bottom = $30 - 11 + 1$

Rank from bottom = $19 + 1$

Rank from bottom = $20$

Both methods give the same result. Aaditya is 20^th from the bottom.

Revision Table: Understanding Ranking Concepts

Additional Information on Ranking Logic

Understanding ranking problems is crucial for logical reasoning sections in many exams. The key idea is that a person's rank from one end determines the number of people before them, and similarly for the other end. When you add the number of people before the person (from one end), the number of people after the person (from the other end), and the person themselves, you get the total number of people.

For instance, if someone is 5th from the top in a line of 10 people:

• There are $5 - 1 = 4$ people above them.
• The total is 10. So, there are $10 - 5 = 5$ people below them.
• Their rank from the bottom is the number of people below them plus themselves: $5 + 1 = 6$th.

Using the formula: Rank from bottom = Total - Rank from top + 1 = $10 - 5 + 1 = 5 + 1 = 6$th.

This consistency helps verify your calculation in ranking problems.