Total number of persons = (Sum of positions of two different persons from both sides) + number of persons between two persons OR 

Number of persons between two persons  = Total number of persons - (Sum of positions of two different persons from both sides)

Example: In a row of 62 persons.  Riya is 24^th from the left side of the row and Raman is 20^th form the right side of the row. Find out the number of persons sitting between them?

Solution: No. of Persons between Riya and Raman = 62 - (24+20)= 62-44 = 18

2) Overlapping case: When (left position of one person+ right position of another person) > Total number of students 

Total number of persons = (R1+R2) - (number of persons between two persons+2) OR

Number of Persons between two different persons = (Sum of positions of two different persons from both sides) -Total no. of Persons –2

Case 3

To find the number of persons after or before a person whose rank is given -

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

Example: In a row of 20 persons, the position of Ritu from the left side of the row is 6^th. Find the no. of persons after Ritu in the row?

Solution: Number of persons after Ritu = Total no. of persons – Position of A from left

⇒ No. of persons after A in the row = 20 – 6 = 14

Case 4 

When in a row, the positions of two persons is given and their positions are interchanged and after interchanging the position of 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 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

Total Number of persons = Sum of the positions of a person (same person) from both sides - 1

Number of persons between two persons = Difference in the positions of a person(same person) whose position from same side before and after interchanging is given -  1

Example: In a row of girls, Pratibha is 15th from the left and Kanika is 23rd from the right. If they interchange their positions, then Pratibha becomes 18th from the left. Then at what position will Kanika be from the right?

 
Total no of girls in a row = Left End + Right End - 1 
= 18 + 23 – 1 = 40 
Kanika’s position from right end = Total girls – Left end + 1 
= 40 – 15 + 1 = 26

Example 2: Rahul and Nitesh are standing in a row of persons. Rahul is 12^th from the left side and Nitesh is 18^th from the right side of the row. If they interchanged their positions Rahul becomes 25^th from left. Find these-

a) New position of Nitesh from the right side

b) Total number of persons

c) Number of persons between them

Solution: A) Rahul Position changes from 12^th to 25^th from the left end. So there is an increase of 13 ranks. Since Rahul and Nitesh both are interchanged their positions so there must be same increase in ranks. So new position of Nitesh from right side= 18 +13= 31

B) In this questions, Rahul position changes from 12 to 25 from left. That means 24 persons are standing from his left side. Now Rahul is at Nitesh’s position which is 18^th from the right side. That means 17 persons are standing from his right. Add all these left and right= 24+17+1(Rahul’s own)=42 total persons

C) Number of persons between Rahul & Nitesh = (Position of Rahul from left after interchanging– Position of Rahul from left before interchanging) – 1 ⇒ No. of persons between Rahul & Nitesh = (25 – 12) – 1 = 13 – 1 = 12

 Case 5

If total no. of persons are asked and positions of two different persons from different sides are given then it is always a case of ‘cannot be determined’. Because we do not know if there will be overlapping or not.

Example: In a row, Position of Raman from left side of the row is 22^nd  and position of Ramesh from right side of the row is 35^th. Find the total no. of students in the row?

Solution: Cannot be determined

Case 6 

If the 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. If total number of persons is to be calculated, then there are two conditions -

1. When the position of third person is given from either side of the row.
2. When the position of the third person is given with respect to either of the two persons between whom he/she is sitting.

Example: In a row of persons, the position of Riya from the left side of the row is 10^th and position of Ranjan from the right side of the row is 9^th. If Mahesh is sitting just in the middle of Riya and Ranjan and position of Mahesh from the left of the row is 16^th. Find the total number of persons in the row?

Sol: Position of Mahesh from left is 16^th and Riya from left is 10^th so there are (16-10-1=5) persons are sitting between Riya and Ranjan. As Mahesh is sitting exactly middle between them so 5 persons sitting between Mahesh and Ranjan. 

Position of Mahesh from right= Position of Ranjan from right 9 + 5 +1= 9+6=15^th 

Total number of persons= Sum of Gaurav’s positions from both sides -1 =(16+15)-1=31-1=30