A class has a total of 60 students. Student 'B' is at 41st rank in merit order from the bottom. What is the rank of student 'B' from the top?
20th
Understanding Class Ranking
This question involves understanding how ranking works in a class of students. We are given the total number of students in a class and the rank of a specific student, 'B', from the bottom of the merit order. We need to find student 'B's rank from the top.
Let's break down the information given:
- Total number of students in the class = 60
- Student 'B's rank from the bottom = 41st
We need to determine student 'B's rank from the top.
Calculating the Rank from the Top
To find the rank of a student from the top when their rank from the bottom and the total number of students are known, we can use a simple formula. The formula accounts for the fact that the student is counted in both the 'from the top' count and the 'from the bottom' count.
The formula is:
Rank from Top = Total Number of Students - Rank from Bottom + 1
Let's apply this formula using the values from the question:
Rank from Top = \(60 - 41 + 1\)
First, subtract the rank from the bottom from the total number of students:
\(60 - 41 = 19\)
This result (19) tells us how many students are *ahead* of student 'B' if we count from the bottom up to the student *just before* 'B'. Alternatively, it tells us how many students are *behind* student 'B' when counting from the top.
Now, add 1 to this result to include student 'B' himself in the count from the top:
\(19 + 1 = 20\)
Therefore, student 'B' is at the 20th rank from the top.
Explanation of the Formula
Consider a small example. If there are 5 students and someone is 2nd from the bottom:
- Total students = 5
- Rank from bottom = 2nd
Students are ordered like this (from top to bottom): S1, S2, S3, S4, S5.
Rank from bottom: S5 is 1st, S4 is 2nd, S3 is 3rd, S2 is 4th, S1 is 5th.
If a student is 2nd from the bottom (S4), their rank from the top is 4th.
Using the formula: Rank from Top = \(5 - 2 + 1 = 3 + 1 = 4\).
The formula works because subtracting the rank from the bottom (\(60 - 41\)) gives you the number of people *below* student 'B'. Adding 1 includes student 'B' himself to find his rank from the top.
| Description | Value |
|---|---|
| Total Students | 60 |
| Student 'B' Rank from Bottom | 41st |
| Calculation: \(60 - 41 + 1\) | \(19 + 1 = 20\) |
| Student 'B' Rank from Top | 20th |
Conclusion
Based on the calculation using the formula, if student 'B' is 41st from the bottom in a class of 60 students, his rank from the top is 20th.
Revision Table: Class Ranking Concepts
| Concept | Explanation | Formula |
|---|---|---|
| Total Students | The total count of individuals in the ranking list. | N |
| Rank from Top | Position counted starting from the first individual. | \(N - \text{Rank from Bottom} + 1\) |
| Rank from Bottom | Position counted starting from the last individual. | \(N - \text{Rank from Top} + 1\) |
Additional Information: Ranking Problems
Ranking problems are common in quantitative aptitude and logical reasoning sections of exams. They often involve determining positions based on relative information. Key things to remember are:
- The total number of items (students in this case) is crucial.
- A person's rank from one end is directly related to their rank from the other end.
- The '+1' in the formula is necessary because the person themselves is included in the count from both ends.
- Problems might involve comparing ranks of multiple people or dealing with people between two ranks.
Always carefully read whether the rank is from the 'top', 'bottom', 'left', or 'right'. The principle usually remains the same regardless of the direction used.
Important Questions from Ordering and Ranking
In a row of people all facing north, Prince is 5th from the right end. Amit is 15th from the right end. Amit is exactly between Prince and Aditya. If Aditya is sixth from the left end of the line, how many people are there in the row?
In a row, Mansi is 29th from the left and 33rd from the right. How many students are there in the row?
A medical representative plans to visit each of six hospitals — A, B, C, D, E and F — exactly once during the course of one day. He is setting up his schedule for the day according to the following conditions:
i. He must visit A before B and E.
ii. He must visit B before D.
iii. The third hospital he visits must be C.
Which of the following could be the possible order in which the medical representative visits the six hospitals?Sonam is older than Renu. Komal is younger than Renu. Priya is older than Sonam. Who is the eldest of them?
Five men P, Q, R, S and T are reading a newspaper. The one who reads it first, gives it to T. The one who reads it last, had taken it from R. Q is not the first or last one to read it. There were two readers between P and R. Who is the third one to have read the newspaper?
