Order and Ranking: Reasoning Concepts

Order and Ranking questions test your ability to determine the position of a person/object based on information such as:

• Rank from the top/bottom
• Position from the left/right
• Number of people between two persons
• Relative positions such as before, after, immediately before, etc.
• Arrangement of people/items in a straight line
• Comparison-based ranking

This topic is closely related to linear arrangement, but here we will exclude seating arrangements such as circular seating, facing directions, etc.

1. Basic Concept of Ranking

A person’s rank can be counted from either:

• Top / Front / Left, or
• Bottom / Back / Right

If the total number of persons is known:$$\boxed{\text{Rank from one end} + \text{Rank from other end} = \text{Total persons} + 1}$$

Therefore:$$\boxed{\text{Total persons} = \text{Rank from left} + \text{Rank from right} – 1}$$

Example

Ravi is 12th from the top and 18th from the bottom.

Find the total number of students.$$12+18-1=29$$

Answer: 29 students

2. Finding Rank from the Opposite End

If the total number of persons and rank from one end are known:

$$\boxed{\text{Rank from opposite end}=\text{Total}-\text{Known rank}+1}$$

Example

There are 40 students in a class. Priya is 15th from the top.

Her rank from the bottom:$$40-15+1=26$$

Answer: 26th from the bottom

3. Why Do We Add/Subtract 1?

This is one of the most common mistakes.

Suppose there are 10 people.

The person who is:

• 1st from the left is 10th from the right.
• 2nd from the left is 9th from the right.

For the same person:$$\text{Left rank}+\text{Right rank}=11$$

That is:$$10+1$$

We add 1 because the person’s own position gets counted from both sides.

4. Number of Persons Between Two Ranked Persons

Suppose two people are ranked from the same direction.$$\boxed{\text{Persons between}=|\text{Rank}_1-\text{Rank}_2|-1}$$

Example

Aman is 8th from the top and Bharat is 15th from the top.

Persons between them:$$15-8-1=6$$

Answer: 6 persons

When Ranks Are Given from Opposite Ends

Suppose:

• A is 8th from the left.
• B is 12th from the right.
• There are 30 persons in total.

First convert both positions to the same side.

B’s position from the left:$$30-12+1=19$$

Therefore, persons between A and B:$$19-8-1=10$$

Answer: 10 persons

5. Finding Total Number When Two Persons Have Given Positions

This is a very important type.

Suppose:

• A is 8th from the left.
• B is 12th from the right.
• There are 5 persons between A and B.

If A is to the left of B, then:$$\text{Total}=8+5+12$$$$=25$$

Why?

The arrangement is:

8th position → A → 5 persons → B → 12 positions from right

So:$$\boxed{\text{Total}=\text{Left rank}+\text{Between}+\text{Right rank}}$$

Answer: 25

Important Condition

This formula works when the two persons are positioned such that their given ranks represent the two outer portions.

For example:

A is 8th from left → 5 people → B is 12th from right

Then total:$$8+5+12=25$$

6. When Two Persons Exchange Positions

Sometimes two people exchange their positions.

Example

In a class of 40 students:

• A is 10th from the top.
• B is 25th from the top.

If they interchange their positions, what will be A’s rank from the bottom?

After interchange, A takes B’s position.

So A becomes:$$25^{th} \text{ from top}$$

Rank from bottom:$$40-25+1=16$$

Answer: 16th from the bottom

7. Rank Changes After Moving Up or Down

Example

Ravi is 20th from the top. He moves up by 5 positions.

New rank:$$20-5=15$$

Answer: 15th from the top

If he moves down by 7 positions:$$20+7=27$$

Answer: 27th from the top

Remember

• Moving towards the top/left/front → rank decreases.
• Moving towards the bottom/right/back → rank increases.

8. Rank Improvement and Deterioration

If a student’s rank improves from 30 to 18:$$30-18=12$$

The student has improved by 12 positions.

If rank changes from 10 to 17, the student has gone down by:$$17-10=7$$

positions.

9. Rank After Adding or Removing People

Case 1: People Are Added Before the Person

Suppose A is 10th from the left. Three people join before A.

New position:$$10+3=13$$

Case 2: People Are Removed Before the Person

If 4 people before A leave:$$10-4=6$$

A becomes 6th from the left.

Case 3: People Are Added After the Person

A’s rank from the left does not change.

However, A’s rank from the right may change.

10. Comparing Heights, Marks, Ages, etc.

Order and ranking questions often use comparisons instead of direct positions.

For example:

A is taller than B.
B is taller than C.

Therefore:$$A>B>C$$

Here, A is tallest and C is shortest.

Example

Five people A, B, C, D and E have different heights.

• A is taller than B.
• B is taller than C.
• D is taller than A.
• E is shorter than C.

Arrange them from tallest to shortest.

Combining:$$D>A>B>C>E$$

Tallest: D
Shortest: E

11. Understanding Comparison Symbols

You can use symbols to simplify questions.

For example:

• A is older than B → $A>B$
• C is younger than B → $C<B$
• D scored more than A → $D>A$

Then combine the information.

Example

• P > Q
• Q > R
• S > P

Therefore:$$S>P>Q>R$$

So S has the highest value and R has the lowest.

12. Finding Position Using Relative Information

Example

Five people A, B, C, D and E are standing in a line.

• A is before B.
• C is after B.
• D is before A.
• E is after C.

Find the order.

Combining:$$D \rightarrow A \rightarrow B \rightarrow C \rightarrow E$$

So, from left to right:

D, A, B, C, E

13. Immediate Before and Immediate After

These words are extremely important.

Immediate Before

If A is immediately before B:$$A-B$$

There is no person between them.

Immediate After

If C is immediately after D:$$D-C$$

Again, no person is between them.

Example

A is immediately before B, and B is immediately before C.

Therefore:$$A-B-C$$

14. “Before” vs “Immediately Before”

These are different.

A is before B

Possible arrangements:

• A X B
• A X Y B
• A B

There can be any number of persons between them.

A is immediately before B

Only:$$A-B$$

No one can be between them.

15. One Person Between / Two Persons Between

If exactly one person is between A and B:$$A\_B$$

There is a difference of 2 positions.

If two persons are between A and B:$$A\_\_B$$

There is a difference of 3 positions.

General Rule

If there are $n$ persons between A and B:$$\boxed{\text{Position difference}=n+1}$$

16. Linear Arrangement – Basic Order

Order and ranking questions may involve arranging people in a straight line.

For example:

Five persons A, B, C, D and E are standing in a row.

• B is immediately after A.
• C is immediately before A.
• D is after B.
• E is before C.

Let’s build the chain:$$E-C-A-B-D$$

So the order is:

E → C → A → B → D

17. Solving Linear Arrangement Using Blocks

Whenever two or more people must remain together, create a block.

Example

A is immediately before B.

Treat them as:$$[AB]$$

If C is immediately after B:$$[A-B-C]$$

Now treat the entire sequence as one block.

This makes complex questions much easier.

Example

Six people A, B, C, D, E and F stand in a line.

• A is immediately before B.
• C is immediately after B.
• D is before A.
• E is after C.

The chain becomes:$$D-A-B-C-E$$

F can occupy the remaining position depending on other conditions.

The key idea is to first identify the fixed chain.

18. “Between” May Not Mean Exactly in the Middle

Suppose:

A is between B and C.

This can mean:$$B \quad A \quad C$$

or:$$C \quad A \quad B$$

It does not necessarily mean that A is immediately between them.

Example

If A is between B and C, possible orders include:

• B X A Y C
• C A B
• B A C

Unless the question says immediately between, multiple arrangements are possible.

19. Immediately Between

If A is immediately between B and C:

Possible arrangements:$$B-A-C$$

or:$$C-A-B$$

A must have B and C on its two sides.

20. From Left / Right Arrangement

When people stand in a line, always choose one consistent direction.

For example:

1 2 3 4 5 6 7

These positions can represent:

For every position:$$L+R=N+1$$

21. Determining Position from Multiple Clues

Example

There are 10 people standing in a line.

• A is 3rd from the left.
• B is 4th from the right.

Find the number of persons between A and B.

First convert B’s position from the left:$$10-4+1=7$$

Therefore:

A = 3rd from left
B = 7th from left

Persons between:$$7-3-1=3$$

Answer: 3 persons

22. Finding a Person’s Position When Total Is Unknown

Sometimes the total number of people can be found using relative positions.

Example

A is 12th from the left and B is 18th from the right. There are 7 people between A and B.

Find the total number of people.

Arrangement:$$12 + 7 + 18$$

Therefore:$$=37$$

Answer: 37

23. When Relative Position Creates a Chain

Example

• A is before B.
• B is before C.
• C is before D.

Therefore:$$A<B<C<D$$

This means the order is fixed:

A → B → C → D

This technique is especially useful when there are many statements.

24. “Not Immediately Before/After”

This creates a restriction.

For example:

A is before B but not immediately before B.

Possible:$$A-X-B$$

Not possible:$$A-B$$

25. End Positions

In a line, there are only two ends:

• Extreme left
• Extreme right

Example

There are 8 people standing in a row.

If A is at one of the ends and B is immediately to the right of A, then A must be at the left end.

Why?

If A were at the right end, there would be no position to its right.

So:$$A-B-\_-\_-\_-\_-\_-\_$$

26. Exactly in the Middle

For an odd number of people:$$\boxed{\text{Middle position}=\frac{N+1}{2}}$$

Example

There are 15 people.

Middle position:$$\frac{15+1}{2}=8$$

So the middle person is 8th from either side.

For Even Number of People

There is no single middle position.

For 10 people, the two middle positions are:

• 5th
• 6th

27. Equal Number of Persons on Both Sides

If a person has the same number of persons on both sides, that person is exactly in the middle.

Example

A has 7 people before him and 7 people after him.

Total:$$7+1+7=15$$

A’s position:$$8^{th}$$

28. Difference in Ranks

Suppose:

• A is 5th from the top.
• B is 17th from the top.

Difference in their positions:$$17-5=12$$

There are:$$12-1=11$$

persons between them.

Remember the Difference

• Position difference = 12
• Persons between = 11

These are not the same.

29. Ranking Based on Marks

Example

In a class:

• A scored more than B.
• B scored more than C.
• D scored more than A.

Who scored second highest?

Order:$$D>A>B>C$$

Answer: A

30. Ranking with Incomplete Information

Sometimes the exact order cannot be determined.

Example

• A is taller than B.
• C is taller than B.

We know:$$A>B$$

and$$C>B$$

But we cannot determine whether A is taller than C.

Possible:$$A>C>B$$

or:$$C>A>B$$

Therefore, A and C cannot be compared based on the given information.

This is a common question type.

31. Finding Who Is in the Middle

Example

Five people A, B, C, D and E have different ranks.

• A is better than B.
• B is better than C.
• D is better than A.
• E is worse than C.

Order:$$D>A>B>C>E$$

The middle person is:

B

32. Arrangement with Fixed Distance

Example

There are 8 positions.

A and B have exactly 3 persons between them.

Therefore, their position difference must be:$$3+1=4$$

Possible position pairs:

• (1, 5)
• (2, 6)
• (3, 7)
• (4, 8)

In reverse order, these are also possible.

This technique is useful in arrangement questions.

33. Position After a Given Number of People

Example

A is 4th from the left.

B is 5 places to the right of A.

Therefore:$$4+5=9$$

B is 9th from the left.

If B is 3 places to the left of A:$$4-3=1$$

B is 1st from the left.

34. “Places Away” vs “Persons Between”

Be careful.

If B is 5 places to the right of A

Position difference = 5.

Example:

A at 3rd → B at 8th.

There are:$$5-1=4$$

persons between them.

If 5 persons are between A and B

Position difference:$$5+1=6$$

These phrases are different.

35. Minimum Number of People Needed

Suppose:

• A is 10th from the left.
• B is 12th from the right.
• There are 5 people between them.

The minimum total required for this arrangement is:$$10+5+12=27$$

This assumes A is before B.

36. Maximum Number of People – When Exact Total Cannot Be Found

Sometimes the information does not fix the total.

Example

A is 5th from the left and B is 7th from the left.

We know their positions, but not the total number of people.

There could be:

• 7 people
• 10 people
• 20 people

Therefore, the total cannot be determined.

Always check whether enough information is provided.

37. A Useful Position Diagram Method

For complex questions, draw boxes.

Example:

1   2   3   4   5   6   7   8
_   _   A   _   _   B   _   _

If A is 3rd from the left and B is 3rd from the right in a group of 8:

B’s position from left:$$8-3+1=6$$

So:

1   2   3   4   5   6   7   8
_   _   A   _   _   B   _   _

This visual method reduces mistakes.

38. Combined Example

Eight people A, B, C, D, E, F, G and H are arranged in a line.

• A is immediately before B.
• C is immediately after B.
• D is before A.
• E is after C.
• F is at the extreme left.

First create the block:$$D-A-B-C-E$$

Since F is at the extreme left:$$F \quad \_ \quad D-A-B-C-E \quad \_ \quad \_$$

The exact positions of G and H may depend on additional conditions.