Ranking and Order — Study Notes

Overview

Ranking and Order problems test your ability to determine the position of individuals or objects in a linear arrangement based on given conditions. In SSC MTS, expect 1–2 questions per paper, making this a scoring topic if you master the method.

These questions typically give you partial information about ranks from the top, bottom, or both ends of a line, or about positions in a sequence. You must calculate missing ranks, total number of people in the line, or relative positions. The key skill is translating verbal statements into mathematical relationships. Unlike complex seating arrangements, ranking questions are straightforward — most can be solved in under a minute using simple formulas and logical deduction.

Mastery requires understanding three core relationships: how top and bottom ranks connect, how overlapping information reveals totals, and how to count people between two positions. Practice 15–20 problems to internalize the patterns, and you'll handle any ranking question confidently on exam day.

Key Concepts

• **Single-line arrangement**: All persons stand in one straight line or queue. Positions are counted from either the left/top end or the right/bottom end.

• **Rank from top vs. rank from bottom**: If someone is 5th from top and 12th from bottom, these two pieces of information together reveal the total number of people in the line.

• **The fundamental formula**: Total = Rank from top + Rank from bottom − 1. The "−1" accounts for the person being counted twice.

• **Persons between two positions**: If A is at position m and B is at position n (both counted from the same end), the number of persons between them is |m − n| − 1.

• **Overlapping ranks**: Sometimes two people swap positions or you're given conditional ranks. Draw a simple diagram or number line to visualize the arrangement.

• **Left-to-right equals top-to-bottom**: In linear arrangements, "from left" and "from top" are interchangeable, as are "from right" and "from bottom" — just directional language.

• **Careful with "including" vs "excluding"**: Questions may ask for positions including or excluding the person in question. Read carefully to avoid off-by-one errors.

Formulas / Key Facts

**1. Total number in line**: Total = Rank from one end + Rank from other end − 1

**2. Rank from bottom when top rank and total known**: Rank from bottom = Total − Rank from top + 1

**3. Rank from top when bottom rank and total known**: Rank from top = Total − Rank from bottom + 1

**4. Persons between two people (same end)**: Between = |Position₁ − Position₂| − 1

**5. Persons between A and B (opposite ends)**: Between = Total − Rank(A from top) − Rank(B from bottom)

**6. If positions interchange**: Carefully update each person's rank from both ends and recalculate total if needed.

**7. When only one end given**: You cannot find the total unless additional information (like "number between") is provided.

**8. Minimum people required**: If A is m-th from top and n-th from bottom, the line must have at least m + n − 1 people (assuming A is the same person counted from both ends).

Worked Examples

**Example 1**: Rahul ranks 7th from the top and 26th from the bottom in a class. How many students are in the class?

*Solution*: Use the formula: Total = Rank from top + Rank from bottom − 1 Total = 7 + 26 − 1 = 32 **Answer: 32 students**

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**Example 2**: In a row of 45 people, Amit is 12th from the left. What is his position from the right?

*Solution*: Use the formula: Rank from right = Total − Rank from left + 1 Rank from right = 45 − 12 + 1 = 34 **Answer: 34th from the right**

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**Example 3**: In a queue, Priya is 15th from the front and Ravi is 18th from the back. If there are 5 people between Priya and Ravi, how many people are in the queue?

*Solution*: Total = Rank of Priya from front + Rank of Ravi from back + People between them Total = 15 + 18 + 5 = 38 **Answer: 38 people**

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**Example 4**: In a class of 40 students, Sita is 16th from the top. If two students ahead of her leave the class, what is her new rank from the top?

*Solution*: Two students ahead leave → Sita moves up by 2 positions New rank from top = 16 − 2 = 14 (New total = 40 − 2 = 38, but question only asks her new rank from top) **Answer: 14th from the top**

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**Example 5**: Anil is 10th from the left and 15th from the right in a row. How many people are between Anil's positions if he were counted from both ends?

*Trick question — testing understanding*: Anil is one person. His rank from left is 10, from right is 15. Total in row = 10 + 15 − 1 = 24 There are 0 people "between" his two counts — he's the same person. **Answer: This question is conceptually flawed as stated; Anil occupies one position. Likely meant to ask total = 24 people.**

Common Mistakes

**Mistake 1**: Forgetting to subtract 1 in the total formula. *Wrong thinking*: Total = Rank from top + Rank from bottom = 7 + 26 = 33 *Correct fix*: The person is counted in both ranks, so Total = 7 + 26 − 1 = 32.

**Mistake 2**: Confusing "people between" with "total positions." *Wrong thinking*: If A is 5th and B is 10th from the same end, there are 5 people between them. *Correct fix*: Between = |10 − 5| − 1 = 4 people. Positions 6, 7, 8, 9 are between 5 and 10.

**Mistake 3**: Using the wrong formula when ends are opposite. *Wrong thinking*: Applying the "between from same end" formula when one rank is from top and other from bottom. *Correct fix*: Use Between = Total − Rank(top) − Rank(bottom) when ranks are from opposite ends.

**Mistake 4**: Not adjusting rank when people leave or join. *Wrong thinking*: If 3 people ahead leave, rank stays the same. *Correct fix*: Rank from top decreases by 3 (you move forward). Rank from bottom changes based on new total.

**Mistake 5**: Misreading "including" vs "excluding" in the question. *Wrong thinking*: "How many people are there from A to B including both?" — counting only those between. *Correct fix*: Including both means add 2 to the "between" count, or use Position(B) − Position(A) + 1 from same end.

Quick Reference

• **Total formula**: Rank(top) + Rank(bottom) − 1 • **Switch ends**: Rank(new end) = Total − Rank(old end) + 1 • **Between (same end)**: |Pos₁ − Pos₂| − 1 • **Between (opposite ends)**: Total − Rank(top) − Rank(bottom) • **People leave ahead**: Your rank from top decreases by that number • **Always subtract 1** when combining ranks from opposite ends to find total — the person is counted twice