Ranking - CSAT Preparation - UPSC

Ranking is an important topic of Reasoning Section for CLAT Examination. Students are usually frequented with the problems based on persons standing in a row or sitting on a bench. Some questions are based on the relative age / height or weight etc. 

Let us discuss some important concepts & approaches of Order and Ranking questions with the help of formulae, tips, and the latest pattern questions.

Important Points for Ranking Questions:

Consider your Left Hand as the Left side and your Right Hand as the Right side.

• In order & ranking, the data related to ranks of a person/persons from the left side/right side, top, bottom are given and the total number of persons are asked. 
• In some questions, the total number of persons are given and rank of the person from the left side, right side, top, bottom are asked. 
• So different types of questions can be formed based on the rank/position of the persons in a row. Generally, four types of questions are formed from this topic which are mentioned as following – 

1. Total number of persons based on the given data
2. The rank of a person from the left or right side
3. Number of persons in between two persons
4. Minimum/Maximum number of persons in a row.
5. The number of persons on either side of a particular person.
6. The rank of a person after interchanging the position
7. Ascending/Descending Order of persons according to their categories (age, height, ranking, marks etc)

Rules to Remember to solve Ranking Questions

• Rule 1: The total number of a person/objects in a group or class is equal to one less than the sum of the positions of the same person from both the ends (either right and left or top and bottom). Since the same person is counted twice in the sum, the final answer is one less than the total sum.

Total number of objects/persons = [(sum of positions of the same person/object from both sides) – 1]

• Rule 2: The total number of person/object in a group is the sum of before or after the given person in a row and the position of the same person from the other side.

Total no. of persons/objects = No. of persons/objects before or after the given person in a row + Position of the same person from the other side.

• Rule 3: If the positions of two objects/persons are given from the opposite ends and also the total number of persons/objects, then the problem can be addressed in two different ways to determine the number of persons between these two persons/objects.

Case 1: Overlapping: The total number of objects or persons in a group is always lesser than the addition of the position of two objects or persons from ends.

Case 2: Non – overlapping: The total number of objects or persons in a group is always greater than the addition of the position of two objects or persons from ends.

• Rule 4: Non-predictable order/ranking.
  If the data in the question provides only then information of position different objects or persons then it is impossible to find the total number of objects or people in a group or class.

 As the cases can either be an overlapping or non-overlapping one. In such a situation, the final answer will always be found. Save the time by not trying to solve these type of questions.

• Rule 5: Swapping of position to find the order/ ranking
  In this section, the placement or the position of the two objects/persons are interchanged. The position of the two people or objects is examined before and after the interchanged.

The place value or the position of the second person from the same side as before interchanging = Position of 2nd person from the same side before interchanging + (Position of 1st person after interchanging – position of 1st person before interchanging from the same side.

• Rule 6: If positions of two objects from opposite sides of the row are known there is a third object right in the middle of the two, then the total number of objects can be evaluated based on the position of the third object.
• Rule 7:
  To find the minimum number of members in the group.

The Minimum number of persons = Sum of positions of persons from both sides – Persons between them – 2.

Solved Examples of Each Type of Questions

TYPE – 1   TO FIND OUT THE POSITION OF A PERSON IN THE ROW FROM LHS/RHS:

To find out the position of a person in a row from right-hand side and left hand side = Number of persons in the row + 1 – Position of the person from the other side.

Example 1:  There are 12 persons in a row. The position of Vipul is 7^th from left. What is his position from the right end?

Ans.  There are total of 12 persons in the row and the position of Vipul is 7^th from left. So there are 5 more persons after him. It means his position is 6^th from the right end

TYPE – 2   TO FIND OUT THE NUMBER OF PERSONS IN THE ROW.

CASE – 1

Given: Position of a person from L.H.S. as well as R.H.S. To find out the number of persons in the row, add up both the positions of the given person and reduce the value by 1.

Example 2: Rohit is standing in a row. His position from the top is 7^th and his position from the bottom is 10^th. How many persons are there in the row?

Sol.: Position of Rohit from both sides is provided to us. To find out the number of persons in the row, we add up both the positions and reduce the final figure by one.

There are six persons ahead of Rohit and nine persons are below him in the row. So the total number of persons in the row is 6 + Rohit + 9 = 6 + 1+ 9 = 16.

CASE – 2  A Given: Position of one is given from the left end and of the other is given from the right end. The number of persons in between them is also given. To find out the total number of persons in the row.

Example 3:  In a row, the position of Vivek is 12^th from left in a row. Sham is 16 positions from right. Ishant is ahead of Vivek by three positions and between Ishant and Sham, there are 5 persons between them. What are the total number of persons in the row?

Ans. Position of Vivek = 12^th from left Position of Sham = 16^th from right

Position of Ishant from Vivek = 3
Persons in between Ishant and Sham =5
Total number of persons = 12 + 16 + 3 + 5 = 36

CASE – 3

Given: Position of one is given from the left end and of the other is given from the right end. The position of person in between them is also given. To find out the total number of persons in the row.

Example 4: The position of Aryan is 12^th from left in a row. Sushant is 16 positions from right. There are 6 persons in between them. What are the total number of persons in the row?

Ans. 
Position of Aryan = 12^th from left  
Position of Sushant = 16^th from right
Persons in between them = 6
Total number of students = 12 + 16 + 6 = 34

CASE – 4

Given:  Position of one is given from the left end and of the other is given from the right end. The number of persons in the row is also given. To find out the total number of persons in between the two given persons.

Example 5: The position of Anurag is 12^th from left in a row. Bajaj is 16 positions from right. There are total of 56 persons in the row. What is the total number of persons in between them?

Ans. Position of Anurag= 12^th from left & Position of Bajaj = 16^th from right

Total number of Persons in the row = 56

Number of persons in between them = 56 – (12 + 16) = 28

CASE – 5

Given:  Position of one is given from the left end and of the other is given from the right end. The position of the two is interchanged and the new ranking is given to them. To find out the total number of persons in the row.

Sol : When the persons interchange their positions, just add the number at “any one position” and deduct “1” from it to get the total number of students.

Example 6:  Marry is 14^th from left and Nancy is 25^th from right. They inter-change their positions. Now Marry is 39^th from left and Nancy is 50^th from right. What is the total number of persons in the row?

Ans. Marry is 14^th from left. At the same position, Nancy is now at 50^th from right. So we add up both the positions and reduce it by one

14 + 50 – 1 = 63

Same result is obtained if we look at the position at the right side. Nancy was 25^th from right and now at the same position Marry is 39^th from left. So we simply add up both the rankings i.e. from left and right and reduce it by one.

25 + 39 – 1 = 63

TYPE – 3 TO FIND THE POSITION OF THE PERSON STANDING IN THE MIDDLE OF

THE ROW

Position of one is given from the left end and of the other is given from the right end. The number of persons in between them is also given. Total number of persons in the row is also given and the student is asked to find the position of a certain person in between them or to find out the ranking of person in their middle

Example 7:   Khushi is 24^th from left in a row and Sharvan is 27^th from right. The total number of persons in the row is 62. Laksh is in the centre of Khushi and Sharvan. What is the position of Laksh from left? Find out his position from right as well.

Ans. Number of persons in between Khushi and Sharvan = 62 – (24 + 27) = 11

Now Laksh is in between the two, so his position is 6^th from either side.

So position of Laksh from left   = 24 + 6 = 30^th

And position of Laksh from right = 27 + 6 = 33^rd

TYPE –4 QUESTIONS BASED ON HEIGHT/AGE/WEIGHT OF PERSONS

FOLLOWING ARE THE STEP TO SOLVE THESE TYPE

Step – 1:       We make use of symbols =, >, < i.e. symbol of equality & inequality to find out the relative position

Step – 2:     We arrange all the given elements in a single row relative to each other.

Step – 3:     After the complete arrangement we can answer the question.

Age/Height / weight of different persons relative to each other is given. The student is asked to find out: 

• Who is tallest / oldest?
• Who is shortest / youngest?
• Who is in between the two given persons? Etc.
  Solution: In these type of questions, we use the symbol > or < to make out, who is taller, bigger or elder.

Steps to solve the questions:

• We make use of the signs of equality and inequality i.e. =, > , < , ≥  and ≤.
• If it is given that B < A, the it can be written that A > B.
• Similarly if it is given that X ≥ Y, it means that either X > Y or X = Y.
• Arrange all the given elements in a single row relative to each other as per the information provided.

Example 8: Jasmine is taller than Megha and Megha is taller than Riya. Who is the tallest?

Ans. Jasmine > Megha > Riya, so Jasmine is the tallest among the three.

QUESTIONS BASED ON SIZE OF TOWN ETC.

Size of town or some other parameter is given. The student is asked to rank the city / town etc. on the basis of that given parameter:

a) Which is largest?    b) Which is smaller?   c) Which is nearer?  Etc.

The questions based on size of town are equivalent to the above cited examples and can be easily solved in the same manner.

Example 9:  Of the five towns, Mumbai is larger than Chandigarh, Chandigarh is larger than Kasauli. Kasauli is smaller than Solan. Solan is not as big as Chandigarh. Banglore is not as big as Mumbai but is bigger than Chandigarh. Which is the smallest city?

Ans. We can solve this case again using signs > and <. Using the method used above, we can put the cities in respect of their size as under:

Mumbai > Chandigarh and Chandigarh > Kasauli

Kasauli < Solan (or Solan > Kasauli) and Solan < Chandigarh (or Chandigarh > Solan)

Banglore < Mumbai (or Mumbai > Banglore),   Banglore > Chandigarh

Now if we arrange these sequences, we find that Mumbai > Banglore > Chandigarh > Solan > Kasauli.  Kasauli being the smallest is our answer.