Order and Ranking
Here is a detailed explanation of the Order and Ranking concepts as covered in your provided PDF, including definitions, formulas, solved examples, and additional practice questions with solutions123.
Detailed Explanation: Order and Ranking
Order and Ranking questions involve arranging people or objects in a specific sequence (such as a line or row) and determining their positions or ranks based on given information. These questions are common in competitive exams and test your ability to analyze and interpret relative positions.
Key Concepts and Formulas
1. Total Number of Persons in a Row
Formula:
$$ \text{Total number of persons} = (\text{Rank from one end} + \text{Rank from the other end}) - 1 $$Example: If a person is 10th from the left and 15th from the right in a row,
$$ \text{Total} = (10 + 15) - 1 = 24 $$Explanation: This formula is used when you know the position of a person from both ends143.
2. Rank from Opposite End
Formula:
$$ \text{Rank from opposite end} = (\text{Total number of persons} - \text{Given rank}) + 1 $$Example: In a row of 40 persons, Q is 23rd from the right. What is Q’s position from the left?
$$ \text{Position from left} = (40 - 23) + 1 = 18 $$Explanation: This formula helps you find a person’s rank from the other end if you know the total number and one rank123.
3. Number of Persons Between Two People
There are two cases:
- Simple (Non-overlapping) Case:
Example: In a row of 52, A is 12th from the right and B is 24th from the left.
$$ \text{Number between} = 52 - (12 + 24) = 52 - 36 = 16 $$- Overlapping Case:
Example: In a row of 30, A is 14th from the right and B is 20th from the left.
$$ \text{Number between} = (14 + 20) - (30 + 2) = 34 - 32 = 2 $$Explanation: Use the overlapping formula if the sum of the ranks from both ends exceeds the total123.
4. Minimum/Maximum Number of Persons
- Minimum: Use the overlapping case formula.
- Maximum: Use the simple case formula.
Example: P is 12th from the left and Q is 15th from the right, with 5 persons between them.
$$ \text{Minimum} = (12 + 15) - (5 + 2) = 27 - 7 = 20 $$$$ \text{Maximum} = (12 + 15) + 5 = 32 $$Explanation: Minimum is for overlapping, maximum for non-overlapping15.
5. Rank of a Person Sitting Exactly Between Two
- Find the number of persons between two people.
- The person in the middle will have half the number of people on either side. Example: In a row of 35, Daisy is 5th from the left and Yashika is 9th from the right.
Lipi is exactly in the middle, so there are 10 people on either side.
$$ \text{Rank of Lipi from right} = 9 + 10 + 1 = 20 $$Explanation: Add the people between and the person themselves to get the rank from the end1.
6. Interchanging Positions
- Find the total number of persons using the common person’s position before and after interchange.
- Calculate the new position of the other person. Example: Prabhas is 15th from the left and Kartik is 23rd from the right. After interchange, Prabhas is 18th from the left.
Kartik’s new position from the right:
$$ \text{Position from right} = (\text{Total} - \text{Left rank before interchange}) + 1 = (40 - 15) + 1 = 26 $$Explanation: Use the formula to find the new position after swapping143.
Solved Examples
1. Total Number of Persons
Question: In a class, Albert ranks 6th from the top and 23rd from the bottom. Find the total number of students. Solution:
$$ \text{Total} = (6 + 23) - 1 = 28 $$2. Rank from Opposite End
Question: In a row of 40, Q is 23rd from the right. What is Q’s position from the left? Solution:
$$ \text{Position from left} = (40 - 23) + 1 = 18 $$3. Number of Persons Between Two
Question: In a row of 52, A is 12th from the right and B is 24th from the left. Find the number of persons between A and B. Solution:
$$ \text{Number between} = 52 - (12 + 24) = 16 $$4. Minimum/Maximum Number of Persons
Question: P is 12th from the left and Q is 15th from the right, with 5 persons between them. Find the minimum number of persons. Solution:
$$ \text{Minimum} = (12 + 15) - (5 + 2) = 20 $$5. Interchanging Positions
Question: Prabhas is 15th from the left and Kartik is 23rd from the right. After interchange, Prabhas is 18th from the left. What is Kartik’s new position from the right? Solution:
$$ \text{Total} = (18 + 23) - 1 = 40 $$$$ \text{Kartik’s new position from right} = (40 - 15) + 1 = 26 $$Practice Questions
1. Total Number
Q: In a row, a person is 8th from the left and 12th from the right. How many people are in the row? A:
$$ (8 + 12) - 1 = 19 $$2. Rank from Opposite End
Q: In a row of 25, a person is 10th from the left. What is their position from the right? A:
$$ (25 - 10) + 1 = 16 $$3. Number Between Two
Q: In a row of 30, A is 7th from the left and B is 12th from the right. How many people are between A and B? A:
$$ 30 - (7 + 12) = 11 $$(Check if overlapping is needed: if $7 + 12 > 30$, use overlapping formula. Here, $19 < 30$, so not overlapping.)
4. Minimum Number
Q: X is 10th from the left and Y is 15th from the right, with 4 people between them. What is the minimum number of people? A:
$$ (10 + 15) - (4 + 2) = 19 $$5. Interchanging Positions
Q: In a row, A is 10th from the left and B is 20th from the right. After swapping, A is 15th from the left. What is B’s new position from the right? A:
$$ \text{Total} = (15 + 20) - 1 = 34 $$$$ \text{B’s new position from right} = (34 - 10) + 1 = 25 $$Summary Table
| Concept | Formula/Approach | Example |
|---|---|---|
| Total number | (Rank from left + Rank from right) - 1 | (10+15)-1 = 24 |
| Rank from opposite end | (Total - Given rank) + 1 | (40-23)+1 = 18 |
| Number between (simple) | Total - (Rank A from left + Rank B from right) | 52-(12+24)=16 |
| Number between (overlap) | (Rank A from left + Rank B from right) - (Total + 2) | (14+20)-(30+2)=2 |
| Minimum number | (Rank A from left + Rank B from right) - (Number between + 2) | (12+15)-(5+2)=20 |
| Maximum number | (Rank A from left + Rank B from right) + Number between | (12+15)+5=32 |
| Interchanging positions | Total = (New left + Old right) - 1; New position = (Total - Old left) + 1 | (18+23)-1=40; (40-15)+1=26 |
Tips
- Always draw a diagram or visualize the row.
- Check if the case is simple or overlapping.
- Use the correct formula based on the question.
- Practice with different types of order and ranking questions.
This comprehensive guide, with explanations, examples, and practice questions, will help you master order and ranking reasoning for any competitive exam123.
Order-and-Ranking.pdf ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎
https://testbook.com/reasoning/order-and-ranking-reasoning ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎
https://www.bankersadda.com/order-and-ranking-in-reasoning/ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎
https://byjus.com/govt-exams/ranking-and-order-logical-reasoning/ ↩︎ ↩︎ ↩︎ ↩︎
https://www.practicemock.com/blog/wp-content/uploads/2021/05/Order-Ranking-Practice-Questions-Free-PDF-1.pdf ↩︎ ↩︎
https://testbook.com/objective-questions/mcq-on-ordering-and-ranking--5eea6a0e39140f30f369e431 ↩︎
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