A class has a total of 30 students. Aaditya is at 11 th rank in merit order from the top. What is the rank of Aaditya from the bottom?
20th
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) = 11th
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 11th position from the top, it means there are 10 students above him.
The total number of students is 30. If Aaditya is at 11th 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 20th.
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 20th from the bottom.
Revision Table: Understanding Ranking Concepts
| Concept | Explanation | Example |
|---|---|---|
| Rank from Top | Position counted starting from the first person. | 1st, 2nd, 3rd... |
| Rank from Bottom | Position counted starting from the last person. | Last, second last, etc. |
| Total Students | The complete count of individuals in the ranking. | In this case, 30 students. |
| Relationship | Total = Rank from Top + Rank from Bottom - 1 | $30 = 11 + \text{Rank from Bottom} - 1$ |
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.
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 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?
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?
