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Logical Reasoning for CLAT

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Chapter - 9

Ranking

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.  

  • In first type of  cases it is required to find:
    • The position of the person in the row from L.H.S. / R.H.S.
    • Number of persons in the row
    • Middle person in the row
    • Questions based on relative height / weight / age 
  • In second type of questions, the persons are required to be arranged in the relative order of age / height or weight etc. 

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.

GIVEN: Total number of persons is given. The position of a person from left is given. To find out it position from R.H.S. 

Ex 1:  There are 12 persons in a row. The position of Vipul is 7th 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 7th from left. So there are 5 more persons after him. It means his position is 6th from the right end.

12+1 – 7 = 6

GIVEN: Total number of persons is given. The position of a person from right is given. To find out the position from left.

Ex 2:  The position of Ram is 11th from right in a row of 50 persons. What is his position from the left end?


Ans. There are total of 50 persons in the row and the position of Ram is 11th   from right. So there are more 39 persons ahead of him. It means his position is 40th   from the left end.

50 + 1 – 11 = 40

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.

Ex 3: Rohit is standing in a row. His position from the top is 7th and his position from the bottom is 10th. 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.

From the above diagram, we observe that 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.

Ex 4: In a row, the position of Vivek is 12th 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 = 12th from left Position of Sham = 16th 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.


Ex 5: The position of Aryan is 12th 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 = 12th from left  
Position of Sushant = 16th 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.

Ex 6: The position of Anurag is 12th 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= 12th from left & Position of Bajaj = 16th 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.


Ex 7: Marry is 14th from left and Nancy is 25th from right. They inter-change their positions. Now Marry is 39th from left and Nancy is 50th from right. What is the total number of persons in the row?


Ans. Marry is 14th from left. At the same position, Nancy is now at 50th 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 25th from right and now at the same position Marry is 39th 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


Ex 8:  Khushi is 24th from left in a row and Sharvan is 27th 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 6th from either side.

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

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

 

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:

 

  1. Who is tallest / oldest?
  2. Who is shortest / youngest?
  3. 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:

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

Ex 9: 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.

Ex 10: Hemant is taller than Sameer. Sameer is shorter than Rayan. Rayan is shorter than Hemant. Who is the shortest?

Ans. Hemant > Sameer , 

Sameer < Rayan (or Rayan > Sameer)

Rayan < Hemant    (or Hemant > Rayan) 

So Hemant > Rayan > Sameer

Hemant is the tallest and Sameer is shortest. So our answer is Sameer.

A  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.


Ex 11: 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.

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