Seating Arrangements Chapter Notes | Quantitative Aptitude for CA Foundation PDF Download

Introduction

• Linear Arrangements: In linear arrangements, individuals or objects are arranged in a straight line, either from left to right or right to left. The conditions provided must be followed while making the arrangements. 
• Circular Arrangements: In circular arrangements, individuals or objects are arranged in a circular manner, facing either inward or outward. Again, all the given conditions must be adhered to while making the arrangements. 

Tips for Solving Seating Arrangement Questions:

• Review the Information: Begin by carefully reviewing the given information to get an idea of the situation involving people or objects. 
• Classify the Information: Determine the usefulness of each piece of information and classify them into definite, comparative, and negative information. 
• Definite Information: This type of information indicates a specific placement, such as "X is sitting on the right end of the bench." 
• Comparative Information: This information compares the positions of individuals or objects without specifying exact placements.
  Example 1: A is sitting second to the right of E. This type of information can be helpful when we can get the definite information about E. 
• Negative Information: Negative information helps eliminate possibilities. 
  Example 2: C is not sitting on the immediate left of A.

Type-1 Linear Arrangement

• In a Type-1 Linear Arrangement, objects or individuals are arranged in a straight line or row along a single axis. The specific order and position of each item are crucial. 
• Directions are given with respect to left and right. 

Steps to Solve Linear Arrangements:
(a) Identify the objects and their names. 
(b) Use a pictorial method to represent the people or objects and their positions. 
(c) Arrange the information with relevant facts and their positions and try to find out the solution. 
(d) Answer the questions based on the arrangement having made. 

Important Terms:

• Between: Refers to an item being sandwiched between two others. 
• Immediate Left: Indicates a position directly to the left, not just anywhere to the left. 

When direction of face is not clear, then we take One Row Sequence

(A) When direction of face is not clear, then we take based on diagram will be as follows:

From the above diagram, it is clear that 
(i) Q, R, S, T are right of P but only Q is the immediate right of P. 

(ii) S, R, Q, P are left of T but only S is the immediate left of T. 

(iii) R, S, T are right of Q only R is the immediate right of Q. 

(iv) R, Q, P are left of S but only R is the immediate left of S. 

(v) S and T are right of R but only S is the immediate right of R. 

(vi) Q and P are left of R but only Q is the immediate left of R. 

(vii) P is the immediate left of Q while T is the immediate right of S. 

(B) When direction of face is towards you, then the diagram will be as follows: 

From the above diagram, it is clear that
(i) Left of P = Q, R, S and T
(ii) Right of T = S, R, Q and P
(iii) Q is immediate left of P; R is immediate left of Q; S is immediate left of R and T is immediate left of S.
(iv) S is immediate right of T; R is immediate right of S; Q is immediate right of R; and P is immediate right of Q.

Two Rows Sequence

Let us see 6 persons seating in two rows.

From the above diagram, it is clear that
(i) A is sitting opposite D
(ii) B is sitting opposite E
(iii) C is sitting opposite F
(iv) D and C are sitting at diagonally opposite positions
(iv) A and F are sitting at diagonally opposite positions.

Example 3: Four Children’s are sitting in arrow. A is occupying seat next to B but not next to C. If C is not sitting next to D ? Who is occupying seat adjacent to D.
(a) B
(b) B and A
(c) Impossible to tell
(d) A
Ans: (d)

Solution: The arrangements as per given information is possible only if C is sitting next to B and D is sitting next to A.
Therefore, two possible arrangements are C, B, A, D, or D, A, B, C
Clearly, only A is sitting adjacent to D:

Example 4: P, Q, R, S, T, U, V and W are sitting in a row facing North.
(i) P is fourth to the right of T
(ii) W is fourth to the left of S
(iii) R and U, which are not at the ends, are neighbours of Q and T respectively.
(iv) W is next to the left of P and P is the neighbour of
Q. Who are sitting at the extreme ends ? 

Solution: From information
(i) We get that there are three persons between P and TXXXP.
In the information (iv), it is given that W is next to the left of P and Q is the neighbour of P. Using the information with (i), we get TXXWPQ.
By the information (ii), TXXWPQXS
By the information (iii),

So, T and S are sitting at the extreme ends.

Example 5: There are Five houses P, Q , R, S, T . P is immediate right of Q and T is immediate left of R and immediate right of P . Q is right of S. Which house in the middle.
(a) P
(b) Q
(c) R
(d) T
Ans: (a)

Solution: According to the question the houses can be arranged as follows. Assuming all houses are facing towards North.

Therefore, house P is middle.

Example 6: Five friends are sitting on a bench. A is to the immediate left of B but on the immediate right of C, D is to the immediate right of B but on the immediate left of E. Who are at the extremes?
(a) A, B
(b) A, D
(c) C, E
(d) B, D
Ans: (c)

Solution: Arrangements according to the question as follows. Assuming all students are facing towards North.

Clearly C and E are the extremes.

Example 7: In a college party, 5 girls are sitting in a row. P is to the immediate left of M and to the immediate right of O. R is sitting to the immediate right of N but to the left of O. Who is sitting in the middle?
(a) O
(b) R
(c) P
(d) M
Ans: (a)

Solution: Arrangements of the question as follows.

Therefore, O is sitting in the middle.

Example 8: Five boys A, B, C, D and E are standing in a row. D is on the immediate right of E, B is on the immediate left of E but on the immediate right of A. D is one the immediate left of C, who is standing on the extreme right. Who is standing in the middle?
(a) B
(b) C
(c) D
(d) E
Ans: (d)

Solution: The sequence of Boys as follows. Assuming all boys are sitting towards North.

There E is standing in the middle.

Circular Arrangement

In this arrangement, some persons are sitting around a circle and they are facing the centre.

1. Left movement is called clockwise rotation.
2. Right movement is called anti–clockwise rotation.
(i) The above presentation is for 4 persons but for any number of persons, the direction is taken in the same manner.
(ii) For rectangular and sequence arrangement, directions are taken as discussed in two rows sequence.

Example 9: (Q Nos. 1 to 3) Study the following Question carefully and answer the given questions.
Four ladies A, B, C and D and Four Gentlemen E, F, G and H are sitting in a circle around a table facing each other .
I. No two ladies or gentlemen are sitting side by side.
II. C, who is sitting between G and E, is facing D.
III. F is between D and A and facing G.
IV. H is to the right of B.

(1) Who is sitting left of A?
(a) E 
(b) F
(c) G
(d) H

(2)  is facing whom?
(a) F
(b) B
(c) G
(d) H

(3) Who is immediate neighbour of B?
(a) G and H
(b) E and F
(c) E and H
(d) F and H

Solution: On the basis of given information in the question, the seating arrangements of the persons are as follows.

(1) (b) Clearly , F is sitting left of A.
(2) (d) Clearly E is facing H.
(3) (a) G and H are neighbours of B.

Example 10: Eight persons A, B, C, D, E, F, G and H are sitting around the circle as given in the figure. They are facing the direction opposite to centre. If they move upto three places anti-clockwise, then.

(a) B will face West
(b) E will face East
(c) H will face North-West
(d) A will face South
Ans: (b)

Solution: Following Seating arrangement is formed from the given in formation.

Clearly B will Face west

Example 11: Five People A, B, C, D and E are seated around a round table. Every chair is spaced equidistant from adjacent chairs. (UPSC (CSAT) 2013)
I. C is seated next to A .
II. A is seated two seats from D.
III. B is not seated next to A.
Which of the following must be true?
I. D is seated next to B.
II. E is seated next to A.
Select the correct from the options given below:
(a) Only I
(b) Only II
(c) Both I and II
(d) Neither I nor II
Ans: (c)

Solution: According to the given information there are possible Seating arrangements.

From the above arrangements. It is clear that D is seated next to B . Also E is next to A.
Clearly both statements I and II are true.

Example 12: Study the following Question carefully and answer the given questions.
Eight friends A, B, C, D,E, F, G and H are sitting in a circle facing the centre, not necessarily in the same order. D sits third to the left of A. E sits to the immediate right of A. B is third to left of D. G is second to the right of B. C is neighbour of B. C is third to left of H. (GIC 2012)

Q1: Who amongst the following is sitting exactly between F and D?
(a) C
(b) E
(c) H
(d) A

Q2: Three of the following four are alike in a certain way based on the information given above and so form a group. Which is does not belong to that group.
(a) DC
(b) AH
(c) EF
(d) CB

Q3: Who amongst the following second to the left of H?
(a) E
(b) B
(c) A
(d) None of these

Q4: Who amongst the following are immediate neighbours of G?
(a) CA
(b) AF
(c) DC
(d) DF

Q5: Who amongst the following is sitting third to the right of A?
(a) F
(b) B
(c) H
(d) C

Solution: Arrangements according to the question is as follows.

Q1: (c), Clearly H is sitting exactly F and D 
Q2: (d) So, CB does not belong to the group.
Q3: (d) Clearly, G is sitting second to the left of H
Q4: (c) Clearly D and C immediate neighbours of G
Q5: (d) Clearly, C is sitting third to the right of A