Order and Ranking
Overview
The concept is simple: you're given information about a person's position in a row, queue, or list and asked to find total number of people, someone's position from the other end, or compare positions.
This topic rewards speed and accuracy. The questions are straightforward if you understand the basic formulas and avoid silly errors with "left-right" or "top-bottom" confusion. Since Clerk-level questions rarely involve more than two people or complex overlapping conditions, mastering the fundamentals here guarantees easy marks in under 30 seconds per question.
The key mental shift: always think of positions as numbers on a number line, not abstract concepts. Position from left + Position from right – 1 = Total. Once this formula becomes automatic, you'll solve most questions in one step.
Key Concepts
- Position from opposite ends: If you know position from one end, position from other end = Total – Given position + 1.
- Finding total when both positions are given: Total = Position from left + Position from right – 1. The "–1" accounts for counting the person twice.
- When positions change after interchange: Track each person separately. If A and B swap, A takes B's original position and vice versa.
- "Between" vs "From": "5 persons between A and B" means 5 people in the gap (total span = 7 including A and B). "A is 5th from left" means A occupies position 5.
- Left-Right / Top-Bottom convention: Left and Top are position 1 side. Right and Bottom are the "other end" side.
- Minimum vs Exact total: If a question says "at least," find the minimum possible value. If positions can overlap (same person counted from both ends), total is smaller.
- Two people, same row: When given positions of two different people, consider whether they could be the same person, or if one is to the left/right of the other.
Key Facts / Formulas
| Scenario | Formula |
|---|---|
| Position from right when left position is known | Right = Total – Left + 1 |
| Position from left when right position is known | Left = Total – Right + 1 |
| Total persons (both positions of same person given) | Total = Left + Right – 1 |
| Persons between A and B | Between = Difference of positions – 1 |
| Minimum total (two people, positions may overlap) | Larger of the two given positions |
| Maximum total (two people, no overlap) | Sum of both positions – 1 |
Quick check: Position values are always ≥ 1 and ≤ Total. If your calculation gives 0 or negative, recheck your setup.
Worked Examples
Example 1: Basic position finding
Problem: In a row of 40 students, Ravi is 15th from the left. What is his position from the right?
Solution:
- Position from right = Total – Position from left + 1
- Position from right = 40 – 15 + 1 = 26th from right
Example 2: Finding total
Problem: Meena is 18th from the left and 14th from the right in a queue. How many people are in the queue?
Solution:
- Total = Left position + Right position – 1
- Total = 18 + 14 – 1 = 31 people
Example 3: Interchange of positions
Problem: In a row of 25 students, A is 10th from left and B is 8th from right. If A and B interchange positions, what is A's new position from left?
Solution:
- Step 1: Find B's position from left = 25 – 8 + 1 = 18th from left
- Step 2: After interchange, A takes B's position
- A's new position from left = 18th
Example 4: Persons between two people
Problem: In a row, P is 12th from left and Q is 18th from left. How many persons are between P and Q?
Solution:
- Persons between = Difference of positions – 1
- Persons between = 18 – 12 – 1 = 5 persons
Example 5: Minimum total calculation
Problem: In a row, A is 15th from left and B is 20th from right. What is the minimum number of students in the row?
Solution:
- Minimum occurs when A and B are the same person
- If same person: Total = 15 + 20 – 1 = 34
- But wait—check if they CAN be the same person (no contradiction given)
- Actually, minimum occurs when the row is just long enough to accommodate both positions
- Minimum total = Maximum of (15, 20) = 20 students (if A is to the extreme right part)
Wait, let me recalculate:
- If A and B can be same: Total = 15 + 20 – 1 = 34
- If A and B are different and A is to B's left: positions don't overlap, need to find arrangement
- Minimum possible = Larger position value when one can be at the extreme = 20
Common Mistakes
- Forgetting the "–1": Writing Total = Left + Right instead of Left + Right – 1. Fix: Remember you count the person twice, so subtract 1.
- Confusing "from left" with "to the left of": "5th from left" means position 5. "5 to the left of X" means 5 positions before X. Fix: Read prepositions carefully—"from" indicates absolute position; "to the left/right of" indicates relative position.
- Miscounting persons between: If A is 5th and B is 10th, students write "5 between" (just subtracting). Correct: 10 – 5 – 1 = 4 persons between. Fix: Always subtract 1 after taking the difference.
- Interchange confusion: After A and B swap, students still use A's original position for further calculations. Fix: Clearly note "A's new position = B's old position" before proceeding.
- Minimum/Maximum mix-up: When asked minimum total with two people, assuming they must be different people. Fix: Unless stated "A and B are different persons," consider the overlap case for minimum.
Quick Reference
- Total = Left + Right – 1 (single person, both positions given)
- Other end position = Total – Given position + 1
- Persons between = |Position difference| – 1
- After interchange: A goes to B's old spot, B goes to A's old spot
- Minimum total (two people) = Larger of the two positions (if they can overlap)
- Always verify: no position can exceed total or be less than 1