Ranking Calculation: Finding Total Students in Class

This problem involves finding the total number of students in a class when given a person's rank from both the top and the bottom.

We are given that Varun is:

• Ranked 34th from the top.
• Ranked 11th from the bottom.

To find the total number of students, we can use a simple formula. The rank from the top includes all the students above that person plus the person themselves. Similarly, the rank from the bottom includes all the students below that person plus the person themselves.

If we simply add the rank from the top and the rank from the bottom (i.e., 34 + 11), we are counting Varun twice – once in the top count and once in the bottom count.

Therefore, the correct formula to find the total number of students is:

Total Students = (Rank from Top) + (Rank from Bottom) - 1

Let's apply this formula using LaTeX notation:

$ \text{Total Students} = (\text{Rank}_{\text{Top}}) + (\text{Rank}_{\text{Bottom}}) - 1 $

Plugging in Varun's ranks:

$ \text{Total Students} = 34 + 11 - 1 $

First, add the ranks:

$ 34 + 11 = 45 $

Now, subtract 1 because Varun was counted twice:

$ 45 - 1 = 44 $

So, there are 44 students in Varun's class.

Alternatively, think of it this way:

• Varun is 34th from the top, meaning there are $34 - 1 = 33$ students ahead of him.
• Varun is 11th from the bottom, meaning there are $11 - 1 = 10$ students behind him.
• The total number of students is the sum of students ahead of Varun, Varun himself, and the students behind him: $33 + 1 + 10 = 44$.

Both methods confirm that the total number of students in the class is 44.