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.
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In a row of 45 students, Ravi is 16th from the left end. What is his position from the right end?
Q2 · Ranking & Order · MEDIUM
Among five friends A, B, C, D and E, A is older than B but younger than C. D is older than E but younger than B. C is older than D. Who is the oldest among them?
Q3 · Ranking & Order · HARD
In a class of 60 students, Seema ranks 12th from the top and Neha ranks 25th from the bottom. If there are 8 students between Seema and Neha, how many students are there who are better than both Seema and Neha?
Q4 · Ranking & Order · MEDIUM
In a queue, Amit is 7th from the front and Sumit is 9th from the back. If they interchange their positions, Amit becomes 15th from the front. How many people are there in the queue?
**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**