# How to solve Order & Ranking questions in Reasoning-Concepts

Ordering and ranking questions in reasoning are very common from any competitive exam point of view. In this type of questions generally, the ranks or positions of a person either of the sides( Left or Right/ Top or Bottom) or the total number of persons are to be found out based on condition given in the question.

In this article step-by-step we will discuss important concepts and formula to solve order and ranking questions in reasoning. Using these simple techniques and short methods you can solve any types of order and ranking questions in minimum time.

These concepts will help you answer quickly Order and Ranking questions in exams like IBPS PO, SBI PO, IBPS RRB, IBPS Clerk, SBI Clerk, IBPS RRB, SSC CGL, SSC CGL, SSC MTS, NICL AO, LIC AAO, SBI Associate Clerk, SBI Associate PO  and others.

For easy understanding of this chapter, We will explain all the concepts and different types of ranking questions in reasoning from recent competitive exam.

#### Types of Order and Ranking questions

According to the structure of the ordering and ranking questions in reasoning, we can divide into two categories.

• Horizontal Ranking Problem(Position Based)

In this type, questions are based on the sitting position of a person in an array of persons. Generally, you need to find out the total number of the persons or the position of a person from either side of the row.

• Vertical Ranking Problem(Rank based)

In this type, questions are asked based on a person’s rank in some group or class. A top and a bottom rank exist in this type of ranking problem.

###### NOTE
1. Concepts and formulas are similar for both horizontal and vertical ranking questions in reasoning i.e. the position of a person in a row or the rank in a group or class.
2. Go through the statement line-by-line and draw the diagram if necessary.
3. Consider your left hand as the left side and your right hand as the right side.

#### Type#1

###### Case#1

If the total number of person is given and you know the position of a person from one of the sides, then the position of the person from the other side–

Position of the person from opposite side=( Total no. of person – Position of the person from given side) + 1

For example,

Q.Aruna ranks twelfth in a class of forty-six. What will be her rank from the last?

Sol. Aruna’s rank from the last = (46 – 12) +1=35

###### Case#2

When the position or rank of a person is given both sides, then the total number of persons is found by

Total no. of persons= (Sum of position of the person from both the sides i.e. left and right side or top and bottom) –1

For example,

Q.Rahul ranked ninth from the top and thirty-eighth from the bottom in a class. How many students are there in the class?

Sol. Total students in the class = (9+38) –1= 46

#### Type#2

When there is a specific number of persons after or before of a person and we have the position of that person from the other side.

Using this formula we find,

Total no.  of persons = No. of persons after or before the given person in a row + Position of the same person from the other side

Or

No. of persons after or before the given person in a row = Total no. of persons – Position of the same person from the other side

For example,

Q. In a row of persons, position of A from the left side of the row is 25th and there are 5 persons after A in the row. Find the total number of persons in the row?

Sol. Number of persons in the row = Number of persons after A + Position of A from the left side

Total number of persons = 25 + 5 = 30

Q. In a row of 16 persons, position of A from the right side of the row is 6th. Find the number of persons before A in the row?

Sol. Number of persons before A = Total number of persons – Position of A from the right side

Number of persons before A= 16 – 6=10

###### NOTE
• In this type of questions, before means left side of the person and after means right side of the person.

#### Type#3

When the positions of the two persons are given from the opposite side and we know the total number of persons and we are asked to find the number of persons in between them.

Such types of problems two possible cases arise when trying to determine the number of persons in between the two persons.

###### Case#1

When no overlapping exists between two persons and we know the total number of persons. In this case, the sum of the positions of the two persons is less than the total number of persons.

No. of persons between the two persons= Total no. of person – (Sum of positions of the two different persons from both ends)

For example,

Q. In a queue, Vijay is fourteenth from the left and Jack is seventeenth from the right, If Vijay be ahead of Jack and there be forty-eight persons in the queue, how many persons are there between Vijay and Jack?

Sol. Here Sum of positions of Vijay & Jack from opposite ends = 14 + 17 = 41 < Total No. of persons in the queue.

Therefore, the number of persons between Vijay & Jack is 48 – (14+17) = 7

###### Case#2

When overlapping exists between the positions of two persons and we know the total number of persons. In such type, the sum of positions of two persons is always greater than the total number of persons.

Number of persons between the two persons= (Sum of positions of the two different persons from both ends) – Total No. of person – 2

For example,

Q. In a queue of sixty persons, Ankit is 34th from the left side and Nishant is 29th from the right side. Find the total number of the person in the row?

Sol. Here Sum of positions of Ankit & Nishant from opposite ends = 34 + 29 = 63 > Total No. of persons in the queue.

So the number of persons between Ankit & Nishant is (34+29) – 60 – 2 = 1

#### Type#4

When the total number of persons is to be asked and positions of the different persons from any side are given, then it always be a case of “Cannot be determined” or “Data inadequate” or “Can not say”. This is because we are not sure that if positions are overlapping or not.

For example,

Q. In a row Position of A from the right side of the row is 12th and position of B from the left side of the row is 22nd. Find the total number of students in the row?

Sol. We cannot find any answer as we have no clue of how many persons are between them and their positions are overlapped or not.

###### NOTE

Similarly, If the number of persons between the two different persons is given, in such type we also cannot find the total number of persons in a row. We cannot determine the answer as two possibilities arise.

For example,

Q. Some boys are sitting in a row. P is sitting fourteenth from the left and Q is seventh from the right. If there are four boys between P and Q, how many boys are there in the row?

Sol. From the diagram, it is clear that the total number of boys may be 15 when Person P and Q are overlapped and 25 when they are not overlapped.

This type of questions comes in a tricky way. If in the above question it is to find how many minimum number of boys can be in a row then the answer must 15 where both positions of the person are overlapped.

#### Type#5

When positions of two persons are given and both positions are interchanged. After interchanging, the new position of the 1st person is given from the same side as before interchanging.

• New position of the 2nd person from the same side as before interchanging = Position of the 2nd person from the same side before interchanging + (Position of the 1st person after interchanging – position of the 1st person before interchanging from the same side)
• To obtain total number of persons, find the person whose position from both sides can be derived from the statement. Add both this positions from opposite ends and subtract 1.
• To find the number of persons between them, subtract the positions of the common person whose positions from the same side before and after interchanging are given then subtract 1.

For example,

Q. In a row of girls, Rita and Monika occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, Rita occupies seventeenth place from the right. Then find

1. How many girls are there in the row?
2. How many girls are between Rita and Monika?
3. New position of Monika from the right side?

Sol.

1. Total no. of girls = (Monika’s position from right before interchanging + Monika’s position from left before interchanging) – 1

From the diagram, it is clear that Monika’s old position is occupied by Rita. Therefore Rita’s new position from the right is Monika’s old position from the right.

Total no. of girls = (Rita’s new position from right after interchanging + Monika’s position from left before interchanging) – 1

Total number of girls = (17 + 10) – 1 = 26

1.  Number of girls between Rita & Monika = (Position of Rita from right after interchanging– Position of Rita from right before interchanging) – 1

Number of girls between Rita & Monika = ( 17– 9 ) –1 = 7

1. New position of Monika from right side = Position of Monika from the left side before interchanging + (Position of Rita from the right side after interchanging – Position of Rita from the right side before interchanging)

New position of Monika from right side = 10 + (17–9) = 18

Or subtract the position of Rita from the right side before interchanging from total number of girls and then add 1.

New position of Monika from right side = 26 – 9 +1 = 18

#### Type#6

When positions of two different persons are given from opposite sides of the row and a third person is sitting exactly in the middle of the two, then the total number of persons in the row is calculated as

###### Case#1

When the position of the third person is given from either side of the row

For example,

1. In a row of boys, position of A from left side of the row is 10th and position of B from right side of the row is 7th. If C is sitting just in middle of A & B. Position of C from left side is 14th. Find the total number of boys in the row?

Sol. Position of C from the left is 14th and A from left is 10th, so there are 14 – 10 – 1=3 boys are sitting between A and C. As C is sitting in between A and B So there must also be 3 boys sitting between B and C.

Therefore, the position of C from right= Position of B from right +3+1=7+3+1=11th

Total Number of boys= Sum of positions of C from both the sides –1

Hence, Total Number of boys=11+14 –1=24

###### Case#2

When the position of the third person is given from either of the two persons between whom the third person is sitting.

For example,

1. In a row of girls, Position of P from the right side of the row is 11th, Q from the left side of the row is 19th. If R is sitting in middle of P and Q and position of R from P is 7th. Find the Total number of the girls in the row?

Sol. Position of R from the right = Position of P from right + Position of R from P= 11+7 =18th

Given R is 7th from P and R is sitting in middle of P and Q then also R is at 7th position away from Q

Position of R from left = Position of Q from left + Position of R from Q = 19 + 7 = 26th

Total no. of girls= (Sum of positions of R from both sides – 1)

Total no. of girls= (18 + 26) – 1 = 44 – 1 = 43

finally, you have learned all the important concepts and tricks to solve Order and Ranking questions quickly in the upcoming exams.