Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples - Aptitude Questions & Answers
Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples is one of the most important topics in Logical Reasoning Explained: Concepts, Tricks, and Practice Questions. In this lesson, you will learn concepts, formulas, shortcuts, solved examples, and aptitude questions with answers. This topic is useful for exams like SSC, Bank, CAT, TCS, and other competitive exams.
Mastering Ranking concepts is essential for aptitude tests and competitive exams. This comprehensive guide covers everything from basic position calculation to advanced interchanging problems, explained with clear formulas, examples, and step-by-step solutions.
Ranking: Complete Guide with Formulas & Examples
What is Ranking?
Ranking is the process of arranging items or individuals in an order based on their relative importance, performance, or merit. In aptitude tests, ranking questions involve determining positions of people/objects in rows, queues, or sequences.
Basic Ranking Concepts
Position Terminology
Understanding the key terms used in ranking problems:
- From Left/Right: Position counted from left or right end of a row
- From Top/Bottom: Position counted from top or bottom of a list
- Total Persons: Complete count of all individuals in the arrangement
- Between: Persons/objects located between two specified positions
Core Formula
The fundamental formula for all ranking problems:
Visual Representation:
Position from left + Position from right - 1 = Total Persons
Types of Ranking Problems
1. Finding Total Number of Persons
When positions from both ends are known, calculate total persons using the core formula.
Formula
(or)
Total Persons = Rank from Top + Rank from Bottom - 1
Example 1: Simple Calculation
Problem: In a class, a girl is 10th from either of the ends. How many students are there in the class?
Solution:
- Position from left = 10
- Position from right = 10
- Total Students = 10 + 10 - 1 = 20 - 1 = 19
Example 2: Different Positions
Problem: In a row of students, Ankur is 18th from the left end and 12th from the right end. Calculate total students.
Solution:
- Position from left = 18
- Position from right = 12
- Total Students = 18 + 12 - 1 = 30 - 1 = 29
2. Finding Position from Left or Right
When total persons and one position are known, find the other position.
Formulas
Position from Right = Total Persons - Position from Left + 1
Example
Problem: In a row of 20 boys, Akul is 8th from the left end. Find Akul\'s position from right.
Solution:
- Total boys = 20
- Position from left = 8
- Position from right = Total - Left + 1
- Position from right = 20 - 8 + 1 = 13
3. Finding Rank from Top or Bottom
Similar to left/right positions but applied to vertical arrangements.
Formulas
Rank from Bottom = Total Persons - Rank from Top + 1
Example
Problem: Aman ranked 10th in a class of 25 students. What is his ranking from bottom?
Solution:
- Total students = 25
- Rank from top = 10
- Rank from bottom = Total - Top + 1
- Rank from bottom = 25 - 10 + 1 = 16
4. Persons Between Two Persons (Without Overlapping)
When sum of positions < total persons, calculate persons between them.
Formula
Condition: (Position A from left + Position B from right) < Total Persons
Example
Problem: In a queue of 30 persons, Amith is 10th from left and Bhanu is 13th from right. Find persons between them.
Step-by-Step:
- Total persons = 30
- Amith from left = 10
- Bhanu from right = 13
- Sum of positions = 10 + 13 = 23
- Check: 23 < 30 (No overlap)
- Persons between = 30 - 23 = 7
5. Persons Between Two Persons (With Overlapping)
When sum of positions > total persons, positions overlap.
Formula
Condition: (Position A from left + Position B from right) > Total Persons
Example
Problem: In a row of 20 people, Samir is 15th from right and Emma is 10th from left. Find persons between them.
Step-by-Step:
- Total people = 20
- Samir from right = 15
- Emma from left = 10
- Sum of positions = 15 + 10 = 25
- Check: 25 > 20 (Overlap exists)
- Persons between = 25 - 20 - 2 = 3
6. Interchanging Positions
When two persons swap positions, determine new positions using relationships.
Method
- Note original positions of both persons
- After interchange, one person\'s new position is given
- Calculate total persons using the known new position
- Find the other person\'s new position
Example
Problem: In a row, Rahul is 8th from left, Surya is 11th from right. After interchange, Rahul becomes 10th from left. Find Surya\'s new position.
Step-by-Step Solution:
- Original positions:
- Rahul from left = 8
- Surya from right = 11
- After interchange:
- Rahul occupies Surya\'s original position
- Surya occupies Rahul\'s original position
- Given: Rahul\'s new position from left = 10
- Calculate total persons:
- Rahul\'s new position from left = 10
- Rahul\'s new position from right = Surya\'s original from right = 11
- Total = 10 + 11 - 1 = 20
- Find Surya\'s new position:
- Surya\'s new position from left = Rahul\'s original from left = 8
- Surya\'s new position from right = Total - Surya from left + 1
- Surya from right = 20 - 8 + 1 = 13
Quick Reference Formulas
All Ranking Formulas
| Problem Type | Formula | Condition |
|---|---|---|
| Total Persons | Left + Right - 1 | Always |
| Position from Left | Total - Right + 1 | Given Total & Right |
| Position from Right | Total - Left + 1 | Given Total & Left |
| Between (No Overlap) | Total - (Left + Right) | Left + Right < Total |
| Between (Overlap) | (Left + Right) - Total - 2 | Left + Right > Total |
Advanced Practice Problems
Problem Set 1: Mixed Problems
Problem 1
In a row of 40 students, Priya is 15th from left. What is her position from right?
Solution:
Position from right = 40 - 15 + 1 = 26
Problem 2
In a class, Ravi\'s rank is 7th from top and 23rd from bottom. How many students?
Solution:
Total = 7 + 23 - 1 = 29
Problem Set 2: Complex Scenarios
Problem 3
In a queue of 50 people, A is 12th from front and B is 17th from back. How many between them?
Solution:
- Sum = 12 + 17 = 29
- 29 < 50 → No overlap
- Between = 50 - 29 = 21
Problem 4
In a row of 25 boys, when two interchange positions, one moves from 8th to 15th from left. What\'s the other\'s original position?
Solution:
- Boy A: Original left = 8, New left = 15
- Difference = 15 - 8 = 7 positions moved
- Boy B\'s original position = 15 + 7 = 22 from left
- Check: 22 from left = 4 from right (25-22+1)
Frequently Asked Questions
How to identify overlapping vs non-overlapping?
If sum of positions (left of one + right of other) is less than total persons, it\'s non-overlapping. If sum is greater than total persons, positions overlap.
Do we include the persons themselves when counting \"between\"?
No, \"between\" always excludes the two reference persons. The formulas automatically account for this.
What\'s the most common mistake in ranking problems?
Forgetting to subtract 1 in the total formula. Remember: Left + Right - 1 = Total, not Left + Right = Total.
How to solve ranking problems faster?
Memorize the core formula and practice visualization. Draw quick diagrams for complex problems.
Frequently Asked Questions
What is Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples?
Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples is an important aptitude topic used in competitive exams that tests your logical reasoning and problem-solving abilities.
Is Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples important for competitive exams?
Yes, Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples is frequently asked in SSC, Bank, CAT, TCS, and other placement exams. It's essential to master this topic for better scores.
How to prepare Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples easily?
Practice solved examples, learn formulas and shortcuts, and attempt practice questions regularly to master Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples.
What are the important formulas in Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples?
Key formulas vary by topic, but generally include basic concepts, shortcuts, and standard problem-solving approaches specific to Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples.
How many questions come from Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples?
Typically 5-10 questions come from Ranking Problems in Logical Reasoning: Concepts, Formulas, and Examples in most competitive exams, making it a high-scoring section.
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