Ranking and order reasoning is a type of logical reasoning in which people or objects are arranged according to their position or rank. It involves identifying relationships such as first or last, higher or lower, and before or after in a sequence. The purpose of this reasoning is to determine the correct order based on the given information.
Rules for Ranking & Order
Rule 1:
We can find the total number in a row when the position of one person or object is known from both the left side and the right side.
Formula: Total number of persons/things = Rank from Left end + Rank from Right end – 1
Example: In a row of girls, the position of Radhika is 38th from the left side of the row, and the position from the right side of the row is 19th. Find the total number of girls in that row.
Solution:
Total no. of persons = (The position of Pooja from the left end + the position of Pooja from the right end) – 1
Therefore, the total no. of person is = (38 + 19) – 1= 57 – 1 = 56
Hence, the total number of girls in that row is 56.
Rule 2:
The rank from the opposite side can be found if the rank from one side and the total number in the row are given.
Formula: Position of a person from the opposite ends= (Total number of persons of that row – Position of the same person/thing from the given side) + 1
Example: In a row of 31 persons, the position of Vicky from the left side of the row is 8th. What is the position of Vicky from the right side of that row?
Solution:
The position of Vicky from the right side is = (The total number of persons of that row – Position of Vicky from the left side) +1
= (31-8) + 1 = 24
Rule 3:
The number of people or things before or after a person can be found using their given rank.
Formula: Number of persons/things after or before the given person/thing in a row = Total no. of persons/things – Position of the same person/thing from another side
Example: In a billing line of 32 persons, the position of Hafiz from the front side of the row is 14th. Find the number of persons after Hafiz in that row?
17, 16, 14, 18, 13
Solution:
Number of persons after Hafiz = Total number of persons – Position of Hafiz from the front side
⇒ Number of persons after Hafiz in the row = 32 – 14 = 18
Hence, 18 persons are there after Hafiz in that row.
Rule. 4:
The total number in a row can be determined if the ranks of two persons or things and the number between them are given.
In, such cases there will be two possible type:
A. Case of Overlapping: When the sum of the positions from both ends is greater than the total number of persons.
Formula: Number of persons between them = (Sum of positions of two different persons/things from both sides) – (Total number of persons/things) – 2
Example: In a row of 22 boys. Ronak is 19th from the left side of the row and Shanky is 9th from the right side of the row. Find out the number of persons sitting between them?
Solution:
Number of persons between Ronak and Shanky = (19+9)-22-2= 28-22-2 = 4
Hence, the number of persons sitting between them is 4.
B. Case of not overlapping: When the sum of the positions from both ends is less than the total number of persons.
Formula: Number of persons between two persons/articles = Total number of persons/articles – (Sum of positions of two different persons/articles from both sides)
Example: In a row of 85 persons. Manya is 24th from the left side of the row and Rashi is 19th from the right side of the row. Find out the number of persons sitting between them?
Solution:
Number of persons between Manya and Rashi = 85 – (24+19) = 85-43 = 42
Hence, there are 42 persons between Manya and Rashi.
Rule 5:
When in a single row, the positions of two persons are given and their positions are interchanged and after interchanging the position of first person is given from the same side as before interchanging.
a) To find the total number of persons of that row:
Formula: Total Number of persons = Sum of the particular positions of a place (different person) from both sides – 1
Example: In a row of persons, Ashish is 11th from the left and Salman is 20th from the right. If they interchange their positions, then Ashish becomes 17th from the left. Find out the total number of persons of that row.
Solution:
Positions of Salman before change + position of Ashish after change – 1
20 + 17 – 1 = 36
Hence, there are 36 persons.
b) To find the new position of the second person from the same side as before interchanging:
Formula: The position of the second person from the same side as before interchanging = The position of the second person from the same side before interchanging + (position of the first person after interchanging – position of the first person before interchanging from the same side
Example: In a row of persons, Ashish is 11th from the left and Salman is 20th from the right. If they interchange their positions, then Ashish becomes 17th from the left. Then, what will be the new position of Salman from the right end?
Solution:
Total no of persons in a row = Position from the right end + Position from the left end – 1
= 20 + 17 – 1 = 36
Salman’s position from right end = Total persons – Ashish’s position from the left end + 1
= 36 – 11 + 1 = 26
Hence, in the new arrangement, the position of Salman is 26th from the right end.
c) To find the number of persons between that two persons:
Formula: 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, Avni is 14th from the left end and Tanmay is 13th from the right end of the row. If they interchanged their positions Avni becomes 19th from the left end. Find the number of persons between them.
Solution:
Number of persons between Avni & Tanmay = (Position of Avni from left after interchanging– Position of Avni from left before interchanging) – 1
⇒ Number of persons between Avni & Tanmay is = (19 – 14) – 1 = 5 – 1 = 4
Rule 6:
In a row, 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 that two person. If total number of persons is to be calculated, then there are will be two conditions –
a) When the position of the third person is to the left side of that person whose position was given from the right side. Or when the position of the third person is to the right side of that person whose position was given from the left side.
b) When the position of the third person is to the left side of that person whose position was given from the left side. Or when the position of the third person is to the right side of that person whose position was given from the right side.
Example: In a row there are some persons, the position of Nishant from the left side of the row is 16th and position of Shikha from the right side of the row is 11th. If Mahesh is sitting just in the middle of Nishant and Shikha and there are two persons between Mahesh and Nishant. Find the total number of persons in the row?
Solution:
A) If Mahesh is to the left of Shikha, then the number of persons in the row will be:
Shortcut Rules:
⇒ Position of 1st person+ Position of 2nd person + twice of the number of people between the third person and any of them (which was given) + 1
⇒ Position of Nishant + Position of Shikha + twice of the number of people between the third person and any of them (which was given) + 1
⇒ 16 + 11 + (2 × 2) + 1 = 32
B) If Mahesh is to the right of Shikha, then the number of persons in the row will be:
Shortcut Rules:
⇒ Position of 1st person+ Position of 2nd person + twice of the number of people between the third person and any of them (which was given) – 3
⇒ Position of Nishant + Position of Shikha – twice of the number of people between the third person and any of them (which was given) – 3
⇒ 16 + 11 – (2 × 2) – 3 = 20
Tips and Tricks:
1. Finding the total number in a row
Total number of persons or things = Rank from the left end + Rank from the right end − 1
2. Finding position from the opposite side
Position from the opposite side = Total number in the row − Position from the given side + 1
3. Finding how many are before or after a person
Number of persons or things before or after = Total number − Position of that person from the other side
4. Case of overlapping positions
When the sum of positions from both sides is greater than the total number in the row:
Number of persons between them = Sum of their positions − Total number − 2
5. Case of non overlapping positions
When the total number in the row is greater than the sum of positions from both sides:
Number of persons between them = Total number − Sum of their positions
6. When a third person sits exactly in the middle of two persons
If the positions of two persons are given from opposite sides and another person sits exactly between them, there are two possibilities while finding the total number:
- The middle person may lie toward the left of the person counted from the right, or toward the right of the person counted from the left.
- Or the middle person may lie toward the left of the person counted from the left, or toward the right of the person counted from the right.
Both cases should be checked to determine the correct total.