Order and Ranking

Order and Ranking questions involve determining the position or rank of individuals in a sequence based on height, weight, marks, age, or other parameters. Sometimes, questions also test the ability to calculate total strength, find the position from the other end, or compare relative positions.

These problems measure logical arrangement skills and quantitative reasoning.


Types of Order and Ranking Problems

TypeDescriptionExample
Simple RankingPosition of a person from top/bottom/left/right is given.A is 7th from the top in a class of 20 students.
Finding Position from Other EndPosition from one end is given; you must find position from the opposite end.A is 5th from the left in a row of 12 → from right, A is 8th.
Finding Total NumberPositions from both ends are given; total number must be calculated.A is 6th from left, 10th from right → total = 6 + 10 – 1 = 15.
Comparison RankingRelative positions of two or more people are compared.A is ahead of B by 3 positions in a race.
Rank After ChangesRank is recalculated after someone joins, leaves, or ties.If one student leaves, how does it affect A’s rank?

Key Formulas

  1. Position from Opposite End
    Position from opposite end = (Total + 1) – Position from given end

  2. Total Number of People/Objects
    Total = (Position from left) + (Position from right) – 1

  3. Middle Position
    Middle = (Total + 1) ÷ 2

  4. Rank Shifts
    When people leave or join, adjust total and apply formulas again.


How to Solve Order and Ranking Questions

  1. Note positions carefully: Mark left/right or top/bottom clearly.
  2. Use formulas directly: Saves time instead of manual counting.
  3. Track relative positions: Translate statements like “A is 2 places ahead of B.”
  4. Check total strength when needed: Apply total formula when both-end positions are given.
  5. Cross-check answers: Substitute back into problem to confirm.

Conceptual Tips and Common Mistakes

  • Direction confusion: Always confirm whether ranking is from top/bottom or left/right.
  • Subtracting 1: When using total = left + right – 1, don’t forget to subtract 1.
  • Relative gaps: “Ahead by 3” means there are exactly 2 people between them.
  • Odd vs Even middle: For odd totals, 1 middle person; for even totals, 2 middle positions.

Examples

Example 1 — Simple Ranking

A is 7th from the top in a class of 20 students.
Answer: From the bottom = (20 + 1 – 7) = 14th.


Example 2 — Finding Total

A is 6th from the left and 10th from the right.
Answer: Total = 6 + 10 – 1 = 15 students.


Example 3 — Relative Position

In a row, A is 12th from the left, and B is 15th from the left. How many people are between them?
Answer: 15 – 12 – 1 = 2 people.


Example 4 — Rank After Change

In a class of 50, A is ranked 10th from the top. If the top 5 students leave, what is A’s new rank?
Answer: A’s position becomes (10 – 5) = 5th.