Calculating Student Rank from Bottom

This problem involves determining the rank of a student from the bottom of the class, given their rank from the top and the total number of students. We are given the total number of students, the rank of the top student, and the relative position of Mahesh with respect to the top student.

Understanding the Given Information

• Total number of students in the class = 40
• Mukesh is the top student, which means Mukesh's rank from the top is 1st.
• Mahesh is five ranks below Mukesh.

Finding Mahesh's Rank from the Top

Since Mukesh is the top student (Rank 1) and Mahesh is five ranks below Mukesh, we can calculate Mahesh's rank from the top by adding 5 to Mukesh's rank.

Mahesh's rank from the top = Mukesh's rank from the top + 5

Mahesh's rank from the top = $1 + 5 = 6$

So, Mahesh is at the 6th position when counted from the top of the class.

Calculating Rank from the Bottom

To find the rank of a student from the bottom of the class, we use a standard formula that relates the rank from the top, the total number of students, and the rank from the bottom.

The formula is:

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

Now, we apply this formula using the total number of students (40) and Mahesh's rank from the top (6).

Mahesh's rank from the bottom = $(40 - 6) + 1$

Mahesh's rank from the bottom = $34 + 1$

Mahesh's rank from the bottom = $35$

Therefore, Mahesh's rank from the bottom in the class is 35th.

Step-by-Step Solution Summary

1. Identify the total number of students: 40.
2. Identify the top student's rank: Mukesh is 1st.
3. Calculate Mahesh's rank from the top: 1 (Mukesh's rank) + 5 (ranks below) = 6th.
4. Use the formula: Rank from bottom = (Total students - Rank from top) + 1.
5. Substitute the values: Rank from bottom = $(40 - 6) + 1$.
6. Calculate the result: $34 + 1 = 35$.

Mahesh's rank from the bottom is 35th.

Revision Table: Key Ranking Concepts

Additional Information: Understanding Ranking Problems

Ranking problems are common in competitive exams and quantitative aptitude tests. They usually involve positions in a line, row, or class. The key is to understand the relationship between a person's position from both ends and the total number of people.

• When you are given a rank, say 5th from the top, it means there are 4 people above you.
• Similarly, if your rank is 10th from the bottom, there are 9 people below you.
• The formula Rank from bottom = (Total - Rank from top) + 1 works because Total - Rank from top gives you the number of people *below* that rank. Adding 1 includes the person themselves to get their rank from the bottom.
• Always be careful about whether the rank given includes the person themselves or is just the number of people before or after them. In standard ranking problems, the rank (like 1st, 5th, 35th) includes the person.
• These problems often test your ability to correctly interpret relative positions (like "five ranks below"). If someone is "five ranks below" rank 1, their rank is 1 + 5 = 6. If they were "five people behind" rank 1, and rank 1 is first, then there are 5 people between rank 1 and that person, placing them at rank 1 + 5 = 6 as well. The phrasing needs careful reading.

Practicing various ranking problems with different phrasings will help you master this topic.