Nitin ranks 23 rd from the top in a class of 42. What will be his rank from the last?
20 th
Understanding Ranking Problems
This question is a typical example of a ranking or order problem. We are given the total number of students in a class and the rank of a specific student (Nitin) from one end (the top). We need to find his rank from the other end (the last).
Calculating Rank from the Last
To find the rank of a person from the last when their rank from the top and the total number of people are known, we use a simple formula. The logic behind this formula is that the total number of people is the sum of the number of people before the person, the person themselves, and the number of people after the person.
Let's define the terms:
- Total number of students = $T$
- Nitin's rank from the top = $R_{top}$
- Nitin's rank from the last = $R_{last}$
The number of students before Nitin from the top is $R_{top} - 1$.
The number of students after Nitin towards the last is $T - R_{top}$.
Nitin's rank from the last will be the number of students after him plus Nitin himself. So, $R_{last} = (T - R_{top}) + 1$.
Alternatively, we can think of it as:
$\text{Total} = (\text{Number of people before Nitin}) + (\text{Nitin}) + (\text{Number of people after Nitin})$
$\text{Total} = (R_{top} - 1) + 1 + (R_{last} - 1)$
$\text{Total} = R_{top} + R_{last} - 1$
Rearranging the formula to find $R_{last}$:
$R_{last} = \text{Total} - R_{top} + 1$
Applying the Formula to Nitin's Rank
In this problem, we have:
- Total number of students ($T$) = 42
- Nitin's rank from the top ($R_{top}$) = 23
Using the formula $R_{last} = T - R_{top} + 1$, we substitute the given values:
$R_{last} = 42 - 23 + 1$
$R_{last} = 19 + 1$
$R_{last} = 20$
So, Nitin's rank from the last is 20 th.
Step-by-Step Calculation
Let's break down the calculation:
- Start with the total number of students: 42.
- Subtract Nitin's rank from the top: $42 - 23 = 19$. This gives the number of students after Nitin.
- Add 1 to include Nitin himself when counting from the last: $19 + 1 = 20$.
This confirms that Nitin's rank from the last is 20 th.
| Parameter | Value |
|---|---|
| Total Students | 42 |
| Nitin's Rank from Top | 23 |
| Formula Used | Total - Rank from Top + 1 |
| Calculation | $42 - 23 + 1$ |
| Result | 20 |
Revision Table: Ranking Concepts
| Concept | Explanation | Formula (if applicable) |
|---|---|---|
| Rank from Top/Front | Position counted starting from the first person. | N/A |
| Rank from Bottom/Last | Position counted starting from the last person. | N/A |
| Total People | The total count of individuals in the arrangement. | Rank from Top + Rank from Last - 1 |
| Finding Rank from Last | Calculating position from the end given rank from the beginning and total. | Total - Rank from Top + 1 |
| Finding Rank from Top | Calculating position from the beginning given rank from the end and total. | Total - Rank from Last + 1 |
Additional Information: Variations in Ranking Problems
Ranking problems can have several variations:
- Finding Total: Given ranks of the same person from both ends, find the total number of people. Formula: Total = Rank from Top + Rank from Last - 1.
- Finding Middle Person: Given ranks of two different people from opposite ends and the total number of people, find the number of people between them. This requires checking if the ranks overlap (sum of ranks > total + 1) or not (sum of ranks <= total).
- Overlapping Ranks: When the sum of ranks of two individuals from opposite ends is greater than the total number of people, their positions overlap.
- Non-Overlapping Ranks: When the sum of ranks of two individuals from opposite ends is less than or equal to the total number of people, their positions do not overlap.
Understanding the position relative to others and the total count is key to solving these types of reasoning questions.
Similar Questions
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Important Questions from Ordering and Ranking
Three persons A, Band Care standing in a queue not necessarily in the same order. There are 4 persons between Aand B, and 7 persons between Band C. If there are 11 persons ahead of Cand 13 behind A, what could be the minimum number of persons in the queue?
In a class of 60 students, where the number of girls is twice that of boys, Kamal, a boy, ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is:
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Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled between Statistics and English?
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