Logical Reasoning is often considered the most scoring section in Indian Railway Recruitment Board (RRB) exams, including NTPC, Group D, and Technician. Among the various topics within Reasoning, Ranking and Ordering holds a significant place. It tests a candidate’s ability to determine the position of a person or an object from the top, bottom, left, or right, or to compare multiple individuals based on attributes like height, weight, or marks.
Introduction to Ranking and Ordering for RRB Exams
Ranking and Ordering involve problems where you are given the position of one or more persons in a row or a sequence and are asked to find the total number of people, the position of a person from the opposite end, or the number of people between two individuals. While these questions might seem simple, they often contain subtle traps—especially in overlapping cases—that can lead to negative marking. Mastering this topic requires a clear understanding of basic formulas and the ability to visualize the arrangements mentally.
Topic Weightage and Importance
In the RRB NTPC (CBT-1 and CBT-2), Group D, and Technician Grade exams, you can expect 1 to 3 questions directly from Ranking and Ordering. Additionally, the concepts learned here are foundational for complex Seating Arrangement and Data Sufficiency problems. Given the high competition, where even 0.25 marks can make a difference, securing these 2-3 marks through conceptual clarity is essential for every aspirant.
Key Concepts and Formulas
To solve Ranking and Ordering questions quickly, you must memorize and understand the logic behind these fundamental formulas:
1. Finding the Total Number of People
When the position of a single person is given from both ends (Left and Right or Top and Bottom):
- Total (T) = (Position from Left/Top) + (Position from Right/Bottom) - 1
Reasoning: We subtract 1 because the same person is counted twice—once from the left and once from the right.
2. Finding the Position from the Opposite End
If the total number of people and the position from one end are known:
- Position from Right = (Total - Position from Left) + 1
- Position from Left = (Total - Position from Right) + 1
3. Interchanging Positions
In these questions, two people swap their seats. If 'A' was at position L1 and after swapping moves to L2, the change in position is (L2 - L1). The same change applies to the second person 'B'.
- Total = (New position of A + Old position of B) - 1
4. Finding the Number of Persons Between Two People
There are two cases here:
- Case 1 (Non-Overlapping): If (Sum of positions of A and B from opposite ends) < Total.
Persons Between = Total - (Position of A + Position of B) - Case 2 (Overlapping): If (Sum of positions of A and B from opposite ends) > Total.
Persons Between = (Position of A + Position of B) - Total - 2
5. Minimum and Maximum Number of Persons
- Maximum Strength: Position of A from left + Position of B from right + Persons between them.
- Minimum Strength (Overlapping): Position of A from one end + Position of B from other end - (Persons between them) - 2.
Solved Examples (Step-by-Step)
Example 1: Finding Total Persons
Question: In a row of students, Ravi is 15th from the left end and 24th from the right end. How many students are there in the row?
Step 1: Identify the given values. L = 15, R = 24.
Step 2: Apply the formula: Total = (L + R) - 1.
Step 3: Total = (15 + 24) - 1 = 39 - 1 = 38.
Answer: There are 38 students in the row.
Example 2: Interchanging Positions
Question: In a row, Amit is 10th from the left and Binny is 15th from the right. If they interchange their positions, Amit becomes 22nd from the left. What is the total number of people in the row?
Step 1: Note Amit's new position from the left = 22.
Step 2: Note Binny's old position from the right = 15. (After interchanging, Amit is now sitting where Binny was).
Step 3: Apply formula: Total = (New Position of Amit + Old Position of Binny) - 1.
Step 4: Total = (22 + 15) - 1 = 37 - 1 = 36.
Answer: The total number of people is 36.
Example 3: Overlapping Case
Question: In a row of 40 people, Rahul is 25th from the left and Suman is 22nd from the right. How many people are sitting between them?
Step 1: Find the sum of positions: 25 + 22 = 47.
Step 2: Compare with Total: 47 > 40. This is an overlapping case.
Step 3: Apply overlapping formula: Persons Between = (Sum of positions) - Total - 2.
Step 4: Persons Between = (47) - 40 - 2 = 5.
Answer: There are 5 people between Rahul and Suman.
Common Mistakes to Avoid
- The "Minus 1" Error: Forgetting to subtract 1 when calculating the total from both ends of the same person.
- Misidentifying Overlap: Failing to check if the sum of positions exceeds the total, leading to using the wrong formula for 'persons between'.
- Direction Confusion: Mixing up 'left of' with 'from the left'. Remember, 'left of A' means moving towards the starting point, while 'from the left' means counting from the start.
- Top/Bottom vs Left/Right: The logic remains the same, but students often get confused when the row is vertical. Treat 'Top' as 'Left' and 'Bottom' as 'Right'.
Practice Questions with Solutions
Q1. In a class of 50 students, Mahesh is ranked 18th from the top. What is his rank from the bottom?
Q2. Suresh is 7th to the left of Rohit in a row of 30 boys. If Rohit is 15th from the left end, what is Suresh’s position from the right end?
Q3. In a queue, Amrita is 11th from the front and Mukul is 25th from the back. If there are 10 people between them, find the maximum number of people in the queue.
Q4. Five friends A, B, C, D, and E are compared by height. A is taller than B but shorter than C. D is shorter than B but taller than E. Who is the tallest?
Q5. In a row of girls facing North, Reena is 10th to the left of Pallavi, who is 21st from the right end. If Malini, who is 17th from the left end, is 4th to the right of Reena, how many girls are there in the row?
Solutions
S1: Rank from bottom = (Total - Rank from top) + 1 = (50 - 18) + 1 = 32 + 1 = 33rd.
S2: Rohit is 15th from left. Suresh is 7th to the left of Rohit, so Suresh is 15 - 7 = 8th from left. Suresh’s position from right = (30 - 8) + 1 = 23rd.
S3: For maximum number: Front + Back + Between = 11 + 25 + 10 = 46.
S4: Height order: C > A > B. Also, B > D > E. Combining them: C > A > B > D > E. The tallest is C.
S5: Pallavi = 21st from Right. Reena = 10th to the left of Pallavi = (21+10) = 31st from Right. Malini is 4th to the right of Reena, so Reena is 4th to the left of Malini. If Malini is 17th from Left, Reena is 17 - 4 = 13th from Left. Total = (Reena's Left position + Reena's Right position) - 1 = (13 + 31) - 1 = 43.
Frequently Asked Questions (FAQs)
Q1: What is the difference between Ranking and Ordering?
Ranking usually refers to finding a specific position in a sequence (like 1st, 10th), while Ordering involves arranging entities based on a comparative attribute (like taller, heavier, or faster).
Q2: How do I know if a case is overlapping?
A case is overlapping if the sum of the individual positions of two people (from opposite ends) is greater than the total number of people in the row.
Q3: Why do we subtract 2 in the overlapping formula?
In overlapping cases, when you add the positions of the two people, you count the two people themselves twice and everyone between them twice. To find just the people between them, you must subtract the two individuals (A and B) and the total count adjustment.
Conclusion and Final Tips
Ranking and Ordering is a logical puzzle that requires patience and a structured approach. To excel in this topic for your RRB NTPC or Group D exams, always try to draw a rough line diagram to visualize the positions. Practice different variations, especially those involving interchanging seats and overlapping scenarios. Remember the golden rule: Total = L + R - 1. Consistent practice will help you solve these questions in under 30 seconds, giving you a competitive edge. Keep practicing, stay focused, and you will definitely crack the reasoning section!
