In numbering and ranking arrangement questions, position/rank of a person from left-right/top-bottom of a row/class is to be determined or rank/position is given & total no. of persons is to be calculated. You may also be asked to determine, using data given, which floor which person lives on.

Note:
1) Read the statement line by line and apply the cases as explained below.
2) Position can be from either sides of row and rank is always from top or bottom of the row
Here, different types of numbering & ranking arrangement questions are explained below with the help of different examples. By grasping each type, you can have a complete command over this topic and ensure 3-5 marks in your kitty.
Number Ranking : TYPE 1 
1) Total number of persons = {(sum of positions of same person from both sides i.e. left and right side) – 1}
OR
2) Position of a person from opposite side = {(Total no. of persons – Position of same person from given side) +1}
Number Ranking E.g.1) In a row of persons, position of A from left side of the row is 27th and position of A from right side of the row is 34th. 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

Ranking E.g. 2) In a row of 16 persons, position of A from left side of the row is 12th. Find the position of A from right side of the row?
Solution:

Position of A from right side = {(Total no. of persons – Position of A from left side) + 1}
⇒Position of A from right side = (16 – 12) + 1 = 4 + 1 = 5th

Number Ranking : TYPE 2
1) Total no. of persons = No. of persons after or before the given person in a row + Position of same person from the other side
OR
2) No. of persons after or before the given person in a row = Total no. of persons – Position of same person from other side
E.g.1) In a row of persons, position of A from left side of the row is 27th 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

Number Ranking E.g.2) In a row of 18 persons, position of A from left side of the row is 6th. Find the no. of persons after A in the row?
Solution:

No. of persons after A = Total no. of persons – Position of A from left
⇒ No. of persons after A in the row = 18 – 6 = 12

Number Ranking : TYPE 3
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 –
When there is no overlapping: i.e. the sum of positions of the two persons from opposite ends < total number of persons
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)
E.g.1) In a row of 54 persons, A is 15th from the left side of the row and B is 20th 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
E.g.1) In a row of 54 persons, A is 35th from the left side of the row and B is 22nd 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

Number Ranking : 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.
Number Ranking E.g. In a row Position of A from left side of the row is 18th and position of B from right side of the row is 25th. Find the total no. of students in the row?
Solution:
Cannot be determined as position of different persons is given from the same side.