RRB Group D Reasoning Ranking Basic To Advance

RRB Group D Reasoning Ranking Basic To Advance is an important topic that helps candidates build strong logical thinking for the exam. Ranking questions test your ability to understand positions in a row, compare individuals, and calculate total numbers using simple formulas. 

From basic concepts like finding a person’s position from left or right to advanced problems involving overlapping cases, interchanging positions, and removal of people, this topic covers a wide range of question types. If you understand the core formulas and practice regularly, Ranking becomes one of the easiest and most scoring sections in RRB Group D Reasoning.

Order and Ranking 

Order and ranking are fundamental reasoning topics in competitive exams, essential for evaluating a candidate's logical and analytical skills. This section demystifies core concepts and problem types, from calculating positions in a single row to understanding complex scenarios involving multiple individuals and position interchanges. Mastering these principles is key to accurately solving related questions.

Ranking Concepts

The topic of Order and Ranking is broadly categorized into two types of problems:

1. Order Sequence: These involve relative comparisons (e.g., "A is taller than B") to determine an overall order or identify extreme positions like tallest or shortest.

2. Ranking Test: These focus on determining a person's position or rank within a row or queue from different reference points (e.g., left, right, top, bottom).

The Fundamental Principle of Ranking

To determine the total number of people in a row using a single person's position, a core formula is applied. Consider a row where person 'C' is 3rd from the left end and also 3rd from the right end. Simply adding these positions (3 + 3 = 6) overcounts the total number of people if the actual total is 5. This is because person C has been counted twice.

The fundamental formula compensates for this double-counting:

Total = (Position from Left) + (Position from Right) - 1

The subtraction of 1 rectifies the double count of the single person.

Also Read: 

• RRB Group D Reasoning Blood Relation
• RRB Group D Reasoning Clock

Type 1: Ranking of a Single Person

This type of problem focuses on finding the total number of people or a person's position from one end when their position from the other end is known.

Core Formulas

The formula remains consistent for both horizontal and vertical arrangements:

1. For a Horizontal Row:

• Total = Left + Right - 1

• Rearranged forms: Left = Total - Right + 1; Right = Total - Left + 1

2. For a Vertical Row:

• Total = Up + Down - 1

• Rearranged forms: Up = Total - Down + 1; Down = Total - Up + 1

Worked Examples

Example 1: Finding the Total

A person's rank is 7th from the top and 26th from the bottom. Find the total number of people.

• Calculation: Total = 7 + 26 - 1 = 32.

Example 2: Finding Position from the Other End (Vertical)

In a class of 100 students, Aditi is ranked 85th from the top. What is her rank from the bottom?

• Calculation: 100 = 85 + Down - 1 => Down = 100 - 84 = 16th.

Example 3: Finding Position from the Other End (Horizontal)

In a row of 24 people, Aryan is 12th from the right end. What is his position from the left end?

• Calculation: 24 = Left + 12 - 1 => Left = 24 - 11 = 13th.

Complex Variant: Relative Positioning

This variant introduces a second person whose position is given relative to the first.

Example 4:

In a class of 35 students, Govind is 6th from the top. Krishna is 7 ranks below Govind. What is Krishna's rank from the bottom?

1. Krishna's rank from top: 6 + 7 = 13th.

2. Krishna's rank from bottom: 35 = 13 + Down - 1 => Down = 35 - 12 = 23rd.

Example 5 (Reinforcement):

In a class of 120 students, Akash is 20th from the top. Shivam is 20 ranks below Akash. What is Shivam's rank from the bottom?

1. Shivam's rank from top: 20 + 20 = 40th.

2. Shivam's rank from bottom: 120 = 40 + Down - 1 => Down = 120 - 39 = 81st.

Comparative Logic in a Fixed-Size Group

Example 6:

In a class of 23 students, Ram is 13th from the top and Shyam is 14th from the top. What are their respective ranks from the bottom?

• For Ram (13th from top): 23 = 13 + Down - 1 => Down = 11th.

• For Shyam (14th from top): 23 = 14 + Down - 1 => Down = 10th.
  Pedagogical Note: In a fixed-size row, a better rank from one end means a worse rank from the other. Ram is 13th from top (better than Shyam's 14th), so he is 11th from bottom (worse than Shyam's 10th).

Type 2: Ranking of Two Persons

This type involves two individuals with a specific number of people between them. There are two scenarios: non-overlapping (maximum) and overlapping (minimum).

Reasoning for "-2" in Overlapping Case: The two individuals whose positions define the 'Left' and 'Right' ranks are counted twice (once in 'Left' and once in 'Right'). Subtracting 2 corrects this double-counting, in addition to subtracting the 'Middle' people.

Worked Examples

Example 1: Finding the Maximum

In a row, Rohan is 19th from the left, Kapil is 31st from the right. There are 6 people between them. Find the maximum number of people.

• Calculation: Total = 19 + 31 + 6 = 56.

Example 2: Finding the Minimum

Using the same data, find the minimum number of people in the row.

• Calculation: Total = 19 + 31 - 6 - 2 = 50 - 8 = 42.

Example 3: Minimum Case (Vertical)

In a row, Rohan is 19th from the top, Kapil is 31st from the bottom. There are 6 people between them. Find the minimum number of students.

• Calculation: Total = 19 + 31 - 6 - 2 = 42.

Determining Overlap When Not Specified

When the total number of people is given, and you need to find the number of people in the middle, you must first determine if it's an overlapping or non-overlapping case.

The Rule: Compare Sum of Ranks to Total

1. Non-overlapping Case: If (Left Rank + Right Rank) < Total. The sum of positions is less than the total, indicating space between them.

• Formula: Total = Left + Right + Middle

2. Overlapping Case: If (Left Rank + Right Rank) > Total. The sum of positions exceeds the total, meaning positions overlap.

• Formula: Total = Left + Right - Middle - 2

Example: Finding Middle Persons

In a row of 62 students, one person is 21st from the left and another is 14th from the right. How many students are between them?

1. Check for Overlap: Sum of Ranks = 21 (Left) + 14 (Right) = 35. Compare to Total: 35 < 62.

• This is a non-overlapping case.

2. Calculation: 62 = 21 + 14 + Middle => 62 = 35 + Middle => Middle = 62 - 35 = 27.

Type 3: Interchanging Positions

This is a very important problem type where two individuals exchange their positions. After the exchange, one person's new position is given, and the goal is to find the total number of people.

Methodology

1. Two individuals (e.g., Person A and Person B) are initially at certain ranks from opposite ends.

2. They interchange places.

3. A new rank for one person (e.g., Person A's new rank from the left) is provided. This new rank corresponds to Person B's original spot.

4. To find the Total, use the new rank of one person and the original rank of the other person (from the opposite side). The formula is a variation of the basic Total = L + R - 1, applied to the same physical spot now described by two different ranks.

Formula: Total = (Person A's New Position from one side) + (Person B's Original Position from the other side) - 1

Worked Example 1

Given: Keshav is 27th from the left, Karan is 32nd from the right. They interchange. After interchange, Keshav is 34th from the left.

• Calculation:

• Keshav's new position (34th from left) is Karan's original spot.

• Karan's original position from the right was 32nd.

• Total = 34 (Keshav's new left) + 32 (Karan's original right) - 1 = 66 - 1 = 65.

Worked Example 2

Given: Punita is 18th from the left, Mithali is 24th from the right. After interchange, Punita becomes 31st from the left.

• Calculation:

• Total = 31 (Punita's new left) + 24 (Mithali's original right) - 1 = 55 - 1 = 54.

(Memory Tip: For interchange problems, to find the Total: 1. Take the new position of the person whose new rank is given. 2. Take the original position of the *other person. 3. Add these two values and subtract 1.*)

Miscellaneous Problems: Position Changes After Removal

These problems involve a person's rank changing after individuals are removed from the front of a queue.

Example 1

Problem: A is 30th from the front. Three people are between A and B, with B after A. If the first 10 people are removed, what is B's new position from the front?

1. B's initial position: 30 (A's pos) + 3 (between) + 1 (B's pos) = 34th.

2. B's new position: 34 - 10 (removed) = 24th.

Example 2

Problem: A is 60th from one end. Three people are between A and B, with B after A. If the first 20 people are removed, what is B's new position?

1. B's initial position: 60 + 3 + 1 = 64th.

2. B's new position: 64 - 20 = 44th.

Example 3

Problem: A is 15th. Three people are between A and B, with B after A. If the first 13 people are removed, what is B's new position?

1. B's initial position: 15 + 3 + 1 = 19th.

2. B's new position: 19 - 13 = 6th.