Solving Ordering and Ranking Arrangement

Ordering and Ranking Arrangement is an important topic from the point of view of SBI, IBPS,  SSC , RBI and other competitive exams.

When we are doing order and ranking we know basically two type of symbols first is greater than(>)and the other one is less than(<). To solve these questions we only know the three things:

Formulas to  determine the positioning of a person

• Left + Right = Total + 1
• Left = Total + 1 – Right
• Right = 1 + 1 – left
• Total = left + Right

Ranking Arrangement

Let discuss about ‘D’

D’s rank from top = 4 and from bottom = 3

Now total rank = 6

Means total rank = (rank from top + rank from bottom) – 1

Now rank from top = (total rank + 1) – rank from both

Rank from bottom = (total rank + 1) – rank from top

Solving the Problems in various Types

Type 1

Total number of persons = (sum of positions of same person from both sides i.e. left and right side) – 1

Example

In a row of persons, position of A from left side of the row is 27^th and position of A from right side of the row is 34^th. Find total no. of persons in the row?

Solution:

Total no. of students = (Position of A from left + Position of A from right) -1

⇒Total no. of students = (27 + 34) – 1 = 61 – 1 = 60

Type 2

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

Example

1. In a row of persons, position of A from left side of the row is 27^th and there are 5 persons after A in the row. Find total no. of persons in the row?

Solution:

No. of persons in the row = Position of A from left + No. of persons after A

⇒ Total no. of persons = 27 + 5 = 32

Type 3

In the questions where it is asked to find minimum no. of persons in a row then it is always a case of overlapping i.e. given positions of persons from either sides overlap each other.

Then ,Minimum no. of persons = Sum of positions of persons from both sides – Persons between them – 2

Example

If position of A from left side of a row is 15^th and position of B from right side of a row is 19^th and only 1 person is sitting in middle of A & B. Find the minimum number of persons that can be seated in this row?

Solution: Total no. of persons = 15 + 19 – 1 – 2 = 31.

Type 4

If total no. of students is to be calculated and positions of different persons from any side are given then it is always a case of ‘cannot be determined’ or ‘data inadequate’ or ‘can’t say’. This is because we do not know if there is overlapping or not.

Example

In a row Position of A from left side of the row is 18^th and position of B from right side of the row is 25^th. Find the total no. of students in the row?

Solution:

Cannot be determined as position of different persons is given from the same side.

Type 5

Positions of two persons is given and their positions are interchanged and after interchanging position of 1^st person is given from same side as before interchanging

• Position of 2^nd person from the same side as before interchanging = Position of 2^nd person from same side before interchanging + (Position of 1^st person after interchanging – position of 1^st person before interchanging from same side)
• To find total no. of students Þ Find the person whose position from both sides can be depicted from the statement. Add both his positions from opposite ends and subtract 1.
• To find no. of persons between them Þ Difference in the position of common person whose position from same side before and after interchanging is given then subtract 1

Example

A and B are standing in a row of persons. A is 18^th from left side of the row and B is 24^th from right side of the row. If they interchange their positions A becomes 31^st from left. Find

1. i) New position of B from right side
   ii) Total no. of persons
   iii) No. of persons between A & B

Solution:

i) New position of B from right side = Position of B from right side before interchanging + (Position of A from left side after interchanging – Position of A from left side before interchanging)

⇒ New position of B from right side = 24 + (31 – 18) = 24 + 13 = 37^th

ii) Total no. of persons = (A’s position from right before interchanging + A’s position from left before interchanging) – 1

⇒ Total no. of persons = (B’s position from right after interchanging + A’s position from left before interchanging) – 1

⇒ Total no. of persons = (24 + 31) – 1 = 55 – 1 = 54

iii) No. of persons between A & B = (Position of A from left after interchanging– Position of A from left before interchanging) – 1

⇒ No. of persons between A & B = (31 – 18) – 1 = 13 – 1 = 12

Type 6

If positions of two different persons are given from opposite sides of the row and a third person is sitting exactly in middle of the two and total no. of persons in the row is to be calculated as

i) When position of third person sitting is given from either side of row

ii) When position of third person is given from either of the two persons between whom he/she is sitting

Then find the position of the 3^rd person from both sides of the row and hence find total no. of persons according to type 1

Example

 In a row of persons, position of A from left side of the row is 9^th & position of B from right side of the row is 8^th.If C is sitting just in middle of A & B and position of C from left side of the row is 15^th. Find the total no. of persons in the row?

Solution:

Position of C from left is 15^th and A from left is 9^th so there are (15 – 9 – 1 = 5) persons are sitting between A and C. As C is sitting in middle of A and B so there must also be 5 persons sitting between B and C.

Thus position of C from right = Position of B from right + 5 + 1 = 8 + 6 = 14^th

Total no. of students = (Sum of positions of C from both sides – 1)

⇒ Total no. of students = (15 + 14) – 1 = 29 – 1 = 28

Type 7

When the positions of two persons are given from opposite ends and we know the total number of persons, then two cases arise when trying to determine the number of persons between these two persons –

1. When there is no overlapping: i.e. the sum of positions of the two persons from opposite ends < total number of persons
2. When there is overlapping: i.e. the sum of positions of the two persons from opposite ends > total number of persons

Case i)
No. of students between two different persons = Total no. of students – (Sum of positions of two different persons from opposite sides)

Example

 In a row of 54 persons, A is 15^th from the left side of the row and B is 20^th from the right side of the row. Find the no. of persons sitting between A and B?

Solution:

Here Sum of positions of A & B from opposite ends = 15 + 20 = 35 < Total no. of persons

∴ No. of persons between A & B = Total no. of students – (Position of A from left + Position of B from right)

⇒ No. of persons between A & B = 54 – (15+20) = 54 – 35 = 19

Case ii)

No. of students between two different persons = (Sum of positions of two different persons from opposite sides) – Total no. of students – 2

Example

 In a row of 54 persons, A is 35^th from the left side of the row and B is 22^nd from the right side of the row. Find the no. of persons sitting between A and B?

Solution:

Here Sum of positions of A & B from opposite ends = 35 + 22 = 57 > Total no. of persons

∴ No. of persons between A & B = (Position of A from left + Position of B from right) – Total no. of students – 2

⇒ No. of persons between A & B = (35+22) – 54 – 2 = 57 – 54 – 2 = 1

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