Ordering and Ranking Arrangement is an important topic from the point of view of SBI PO, SBI Clerk, IBPS PO, IBPS Clerk, SSC, CAT and many other competitive exams. There are usually 3-5 questions in any exam from this topic. By following some simple shortcut tricks, you can easily crack the questions in a matter of seconds. This can be helpful in boosting your reasoning ability and, more importantly, your marks in the exam. Time is an important factor in qualifying through these competitive exams, and short tricks are the only way to go about getting through the Reasoning section with ease.
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In ordering 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 ordering & 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.
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}
E.g.1) 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
E.g. 2) In a row of 16 persons, position of A from left side of the row is 12^{th}. 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 = 5^{th}
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 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
E.g.2) In a row of 18 persons, position of A from left side of the row is 6^{th}. 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
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 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
E.g.1) 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
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.
E.g. 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
E.g. 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
- 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
E.g. 1) 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
E.g. 2) In a row of persons, Position of A from left side of the row is 11^{th} and B from right side of the row is 19^{th}. If C is sitting just in middle of A & B and position of C from A is 7^{th}. Find total no. of persons in the row?
Solution: Position of C from Left = Position of A from left + Position of C from A = 11 + 7 = 18^{th}
Given C is 7^{th} from A and C is sitting in middle of A and B then also C is at 7^{th} position from B
Position of C from right = Position of B from right + Position of C from B = 19 + 7 = 26^{th}
Total no. of students = (Sum of position of C from both sides – 1)
⇒ Total no. of students = (18 + 26) – 1 = 44 – 1 = 43
Type 7
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
E.g. 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 8
These are ordering type questions. In this type of question, it is given that there are several people living in an n-storey building. Some information will be given about the relative positions of one above or below the other. You need to find which floor each person lives on. These are almost similar to seating arrangement questions. However, you may be required to apply the rules you learnt above, in these problems.
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