Ranking and Order
About 6 min · Reasoning Ability · English
Time worked out from the lesson's 411 words at 150 words a minute, plus a minute for each question.
Ranking and Order problems test your ability to determine the position of a person or object in a linear arrangement based on given conditions.
Key ideas
- Rank from Left vs Right: Position from left counts starting from the leftmost as 1; position from right counts starting from the rightmost as 1. These are complementary measures.
- The Fundamental Formula: If a person is at position L from left and position R from right in a row of N people, then L + R = N + 1. This single relationship solves most problems.
- Persons Between Two Positions: If two people are at positions P₁ and P₂ (where P₂ > P₁), the number of persons between them = P₂ − P₁ − 1.
- Interchange of Positions: When two people swap seats, their individual ranks change but the total count remains same. Track each person's new position carefully.
- Same Person, Two Ranks Given: When both left and right ranks of the same person are given, directly apply L + R = N + 1 to find total.
Watch out for
- Forgetting the "−1" in the total formula: Students write N = L + R instead of N = L + R − 1. The person themselves gets counted twice if you just add, so subtract 1.
- Confusing "between" with "including endpoints": Between 9th and 16th position means positions 10 to 15, which is 6 people—not 8. Don't count the two endpoint positions.
- Not considering both cases in ambiguous problems: When two different people's positions are given, they could be arranged in two ways (one left of other, or vice versa). Check if both cases yield valid positive answers.
Quick reference
- Total = Left position + Right position − 1
- Other end position = Total − Given position + 1
- Between two positions = Larger − Smaller − 1
- Interchange swaps positions, not ranks—recalculate both positions after swap
- Two cases possible when two different persons' partial positions given
Check yourself: 3 questions
1. In a row of 45 students, Ravi is 15th from the left end. What is his position from the right end?
2. Amit ranks 12th from the top and 28th from the bottom in a class. How many students are there in the class?
3. In a queue of children, Priya is 9th from the left and Kavita is 12th from the right. When they interchange their positions, Priya becomes 21st from the left. What is the total number of children in the queue?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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