Ranking & Order — Study Notes for UP Police Constable

Overview

Ranking and Order questions test your ability to understand positions in a sequence and solve logical puzzles involving arrangements. In the UP Police Constable exam, these questions typically appear in 2–4 forms: finding a person's rank from top or bottom, determining positions after rearrangement, solving age-based ordering problems, and analyzing linear or circular seating sequences.

This topic demands careful attention to detail and systematic problem-solving rather than complex calculations. Students often lose marks here not due to difficulty but due to hasty reading or calculation errors. The good news: once you master the basic techniques, these become scoring questions that can be solved quickly.

Mastering Ranking & Order is essential because it forms the foundation for more complex reasoning topics like seating arrangements and scheduling. Expect 2–3 direct questions from this topic in your exam, making it a reliable source of marks if you practice systematically.

Key Concepts

• **Position from Top and Bottom**: If a person ranks Rth from top and Sth from bottom in a queue, total persons = R + S - 1. The "-1" accounts for counting the person twice.

• **Position Interchange**: When two people swap positions, their new ranks can be determined by careful tracking. If A (5th from top) and B (12th from top) exchange, A becomes 12th and B becomes 5th.

• **Overlapping Information**: When someone's position from both ends is given, you can calculate total members. When finding someone's new position after others leave/join, adjust the count accordingly.

• **Age Ordering**: Questions may ask you to determine relative ages based on comparative statements (A is older than B, C is younger than D). Draw a simple linear diagram with youngest on left, oldest on right.

• **Seating Sequences**: Linear arrangements (row seating) differ from circular ones. In linear: left-right matters and has endpoints. In circular: only relative positions matter, no fixed start/end.

• **Bidirectional Ranking**: Some queues face different directions. "5th from left" when facing north differs from "5th from left" when facing south—directions reverse.

• **Elimination Method**: When multiple conditions are given, systematically eliminate impossible arrangements until only one valid sequence remains.

Formulas / Key Facts

• **Total = Rank from Top + Rank from Bottom - 1**: This is the most frequently used formula. Memorize it.

• **Between Two Persons**: Number of people between A (position P) and B (position Q) = |P - Q| - 1 (when in same row/line).

• **After N people leave from top**: If someone was Rth from top, after N leave from top, new rank = R - N (if R > N).

• **After M join at bottom**: If someone was Sth from bottom, after M join at bottom, new rank = S + M.

• **Circular Arrangement**: For n people in circle, person opposite to Pth position = P + n/2 (when n is even).

• **Position swap formula**: If A is Xth and B is Yth, after swapping A becomes Yth and B becomes Xth.

• **Age comparison chains**: If A > B, B > C, then automatically A > C (transitive property).

• **Linear row neighbors**: If X is 7th from left, person immediately right is 8th from left, immediately left is 6th from left.

Worked Examples

**Example 1: Basic Ranking from Both Ends**

Question: In a class, Rohit ranks 7th from the top and 26th from the bottom. How many students are in the class?

Solution:

• Rohit's rank from top = 7
• Rohit's rank from bottom = 26
• Total students = 7 + 26 - 1 = 32
• Answer: 32 students

**Example 2: Position After Interchange**

Question: In a row of 40 students, A is 12th from the left and B is 15th from the right. If they interchange positions, what is A's new position from the right?

Solution:

• B is 15th from right, so B is (40 - 15 + 1) = 26th from left
• After interchange, A takes B's original position
• A's new position = 15th from right
• Answer: 15th from right

**Example 3: Age Order Puzzle**

Question: Among five friends P, Q, R, S, T: P is older than Q but younger than R. S is the oldest. T is older than P but younger than R. Arrange them by age from youngest to oldest.

Solution:

• S is oldest → S at rightmost
• Relationships: Q < P < R and P < T < R
• Combined: Q < P < T < R < S
• Final order (youngest to oldest): Q, P, T, R, S
• Answer: Q is youngest, S is oldest

Common Mistakes

**Mistake 1: Forgetting to subtract 1 in the formula** Wrong: Total = Rank from top + Rank from bottom = 10 + 15 = 25 Correct: Total = 10 + 15 - 1 = 24. The person is counted once from each end, so subtract 1.

**Mistake 2: Confusing left-right with top-bottom** Wrong: Treating "3rd from left" same as "3rd from top" in different contexts. Correct: Always note whether the arrangement is horizontal (left-right) or vertical (top-bottom). Draw a quick diagram.

**Mistake 3: Direction reversal errors in bidirectional queues** Wrong: Assuming positions remain same when people turn around. Correct: When a row of people turns 180°, the person who was 5th from left becomes 5th from right (if total is known, recalculate).

**Mistake 4: Incorrect calculation when people join/leave** Wrong: If 3 people leave from top and someone was 10th, thinking new rank is 10 + 3 = 13. Correct: When people leave from top, ranks decrease. New rank = 10 - 3 = 7th from top.

**Mistake 5: Misinterpreting "between" in counting** Wrong: Between 5th and 10th positions means 10 - 5 = 5 people. Correct: Between 5th and 10th means 10 - 5 - 1 = 4 people (positions 6, 7, 8, 9).

Quick Reference

• **Total members = Rank from one end + Rank from other end - 1**
• **People between X and Y = |X - Y| - 1**
• **Draw simple diagrams—visual representation prevents errors**
• **After swapping, check what changes (position from top/bottom/left/right)**
• **Age problems: use inequality chains (A > B > C) on paper**
• **In circular seating, opposite person (even total) = Position + n/2**