Number Ranking :TYPE 5
Positions of two persons is given and their positions are interchanged and after interchanging position of 1st person is given from same side as before interchanging

Position of 2nd person from the same side as before interchanging = Position of 2nd person from same side before interchanging + (Position of 1st person after interchanging – position of 1st 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

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

i) New position of B from right side

ii) Total no. of persons

iii) No. of persons between A & B

Explanation

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 = 37th

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

Number Ranking :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

1. i) When position of third person sitting is given from either side of row
2. 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 3rd person from both sides of the row and hence find total no. of persons according to type 1

E.g. 1) In a row of persons, position of A from left side of the row is 9th & position of B from right side of the row is 8th.If C is sitting just in middle of A & B and position of C from left side of the row is 15th. Find the total no. of persons in the row?

Position of C from left is 15th and A from left is 9th 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 = 14th

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

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

E.g. 2) In a row of persons, Position of A from left side of the row is 11th and B from right side of the row is 19th. If C is sitting just in middle of A & B and position of C from A is 7th. Find total no. of persons in the row?