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All questions of Seating Arrangement for SSC CHSL Exam

PASSAGE -1
Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary. 
Q. Who is sitting immediate right to Reeta?
  • a)
    Bindu
  • b)
    Rani
  • c)
    Mary
  • d)
    Seema
Correct answer is option 'C'. Can you explain this answer?

Arya Roy answered
According to the given information, Seema is to the left of Rani and to the right of Bindu. This means that the order from left to right is: Bindu, Seema, Rani.
Mary is to the right of Rani. Therefore, the order from left to right is now: Bindu, Seema, Rani, Mary.
Reeta is between Rani and Mary. This means that Reeta is sitting between Rani and Mary. Therefore, the order from left to right is: Bindu, Seema, Rani, Reeta, Mary.
So, Mary is sitting immediate right to Reeta.

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.
Additional Information:
1. No two persons wearing blue shirts sit on consecutively numbered chairs.
2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.
3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.
4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.
5. Persons wearing red shirts are not sitting at extreme ends.
The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".
Q. Which of the following is not a permissible group of four persons such that the number of persons wearing a red, a green and a blue shirt is 2, 1 and 1 respectively?
  • a)
    K, A, N and Z 
  • b)
    N, Q, K and Z
  • c)
    A, P, L and R 
  • d)
    B, L, M and Q
Correct answer is option 'A'. Can you explain this answer?

Let the people who wear a blue, red and green shirt be denoted by b, r and g respectively. Restrictions on the seating arrangement:
1. Two b’s must not be together.
2. Three r’s must be together.
3. A ‘b’ and a ‘g’ must not be together.
4. A ‘g’ cannot sit on a chair numbered 2 or 9.
Case I: A person wearing a green shirt is sitting on chair numbered 1. It is only possible if another person wearing a green shirt sits on chair numbered 2, but this violates restriction number 4. Hence, this is also not possible.
Case II: A person wearing a blue shirt sits on chair numbered 1. The six seating arrangements that are possible are as follows.

Now, we see that the cases 4, 5 and 6 are just obtained by reversing the cases 1, 2 and 3 respectively. It can be concluded that in any possible seating arrangement, the chairs numbered 1 and 10 are always occupied by people wearing blue shirts. It is given that the number of people wearing a blue shirt is 3. Looking at the table given in the question, we observe that in each of the six arrangements two out of the three different people i.e. A, B and N always sit on chairs numbered 1 and 10.
Hence it can be concluded that the people who wear a blue shirt are A, B and N From the given table the person wearing a blue shirt can never sit on chairs numbered 2, 4, 7 and 9. So, (in arrangement I), A, B and N sitting on chairs numbered 1, 7 and 10 is inconsistent. Also, the people wearing red shirts sit on chairs numbered 2 and 9 and in all the possible arrangements five different people namely P, Q, M, Z and R are sitting on chairs numbered either 2 or 9. Therefore, P, Q, M, Z and R are wearing red shirts and K and L are wearing green shirts.
Option (1): A (Blue), P (Red), R (Red) and L (Green): Permissible
Option (2): N (Blue), Q (Red), K (Green) and Z (Red): Permissible
Option (3): K (Green), A (Blue), N (Blue) and Z (Red): Not Permissible
Option (4): B (Blue), L (Green), M (Red) and Q (Red): Permissible.

Can you explain the answer of this question below:
PASSAGE -1
Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.

Who is in the middle of the photograph ?

  • A:Bindu
  • B:Rani
  • C:Reeta
  • D:Seema

The answer is B.

Alok Verma answered
The number of Girls are 5. They are seema, rani, reeta, mary and bindu
Seema is to the left of rani. So arrangement is:
⇒ Seema, ..., Rani
Seema is to the to the right of bindu. So,arrangement is:
⇒ Bindhu , .. , Seema
Mary is to the right of rani. So arrangement is:
⇒ Rani, ..., Mary
Reeta is between rani and mary. So arrangement is:
⇒ Rani Reeta Mary
So, the arrangement in photograph from left to right side  is:-
Bindu , Seema , Rani , reeta and Mary

These questions are based on the following information. P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R.
Q. Which of the following cannot be the correct seating arrangement of the five persons in either the clockwise direction or the anti-clockwise direction?
  • a)
    P, Q, R, S, T
  • b)
    P, S, R, T, Q
  • c)
    P, Q, S, R, T
  • d)
    P, T, R, S, Q
  • e)
    None of the above
Correct answer is option 'A'. Can you explain this answer?

Tanishq Shah answered
P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

We will take each choice and see whether it fits in the arrangement that we represented through a diagram in the analysis of the data (the same diagram is reproduced below).

We can see that the arrangement given in choice (a) is not possible and hence the answer choice is (a).

These questions are based on the following information. P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R.
Q. If S sits in between Q and R, who sits to the immediate right of P?
  • a)
    R
  • b)
  • c)
  • d)
    T
Correct answer is option 'D'. Can you explain this answer?

Prateek Datta answered
P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

If S sits between Q and R, then the arrangement is as follows.

As can be seen from the diagram, T is to the immediate right of P. Choice (a)

Directions to Solve
Each of these questions are based on the information given below:
  1. A ,B, C, D and E are five men sitting in a line facing to south - while M, N, O, P and Q are five ladies sitting in a second line parallel to the first line and are facing to North.
  2. B who is just next to the left of D, is opposite to Q.
  3. C and N are diagonally opposite to each other.
  4. E is opposite to O who is just next right of M.
  5. P who is just to the left of Q, is opposite to D.
  6. M is at one end of the line.
Question -
If B shifts to the place of E, E shifts to the place of Q, and Q shifts to the place of B, then who will be the second to the left of the person opposite to O ?
  • a)
    Q
  • b)
    P
  • c)
    E
  • d)
    D
Correct answer is option 'A'. Can you explain this answer?

Saranya Ahuja answered
Given Information:
- 5 men (A, B, C, D, E) sitting in a line facing south
- 5 women (M, N, O, P, Q) sitting in a line facing north parallel to the first line
- B, who is just next to the left of D, is opposite to Q
- C and N are diagonally opposite to each other
- E is opposite to O who is just next right of M
- P, who is just to the left of Q, is opposite to D
- M is at one end of the line

Solution:
To solve this question, we need to redraw the diagram after the given changes and then find the person who will be second to the left of the person opposite to O.

New Diagram:
1. Before Changes:
- A B C D E (facing south)
- M N O P Q (facing north)
2. After Changes:
- A Q C B D E (facing south)
- M N E P O (facing north)

Answer:
According to the new diagram, we can see that:
- E is opposite to P
- Q is opposite to B
- O is opposite to C
Therefore, the person opposite to O is C and the person second to the left of C is Q. Hence, the correct answer is option A (Q).

Directions to Solve
Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.
Question -
Who is second from the right ?
  • a)
    Mary
  • b)
    Rani
  • c)
    Reeta
  • d)
    Bindu
Correct answer is option 'C'. Can you explain this answer?

Explanation:

To solve this problem, we need to analyze the given information and determine the order in which the girls are sitting on the bench. Let's break down the given information step by step:

Step 1: Seema is to the left of Rani and to the right of Bindu.
This means that the order of the girls from left to right is Bindu, Seema, and Rani.

Step 2: Mary is to the right of Rani.
Since Rani is on the right end of the bench, Mary must be sitting to the right of Rani.

Step 3: Reeta is between Rani and Mary.
Since Mary is to the right of Rani, Reeta must be sitting between Rani and Mary.

Final arrangement:
Based on the given information, we can determine the following arrangement of the girls from left to right on the bench:
Bindu - Seema - Rani - Reeta - Mary

Answer:
According to the given arrangement, the girl who is second from the right is Reeta (option C).

These questions are based on the following information. P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R.
Q. If S is not sitting next to Q, who is sitting between Q and S?
  • a)
  • b)
    P
  • c)
  • d)
    Both (R) and (P)
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

If S is not next to Q, then the seating arrangement is fixed as follows.

Now P is between Q and S. Choice (b)

Directions to Solve
Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.
Question -
Who is second from the left in photograph ?
  • a)
    Reeta
  • b)
    Mary
  • c)
    Bindu
  • d)
    Seema
Correct answer is option 'D'. Can you explain this answer?

Explanation:

To solve this problem, we need to analyze the given information and determine the position of each girl on the bench.

Given Information:
- Seema is to the left of Rani and to the right of Bindu.
- Mary is to the right of Rani.
- Reeta is between Rani and Mary.

Let's break down the given information step by step:

Step 1:
- Seema is to the left of Rani and to the right of Bindu.
- This means that the order from left to right is Bindu, Seema, Rani.

Step 2:
- Mary is to the right of Rani.
- Since Rani is already seated, Mary will be seated to the right of Rani.

Step 3:
- Reeta is between Rani and Mary.
- Since Mary is to the right of Rani, Reeta will be seated between Rani and Mary.

Now, let's arrange the girls on the bench based on the given information:

Bindu - Seema - Rani - Reeta - Mary

The question asks us to find the girl who is second from the left in the photograph.

Answer:
- The girl who is second from the left in the photograph is Seema (Option D).

Directions to Solve
Six friends are sitting in a circle and are facing the centre of the circle. Deepa is between Prakash and Pankaj. Priti is between Mukesh and Lalit. Prakash and Mukesh are opposite to each other.
Question -
Who is sitting right to Prakash ?
  • a)
    Mukesh
  • b)
    Deepa
  • c)
    Pankaj
  • d)
    Lalit
Correct answer is option 'D'. Can you explain this answer?

Explanation:

To solve this question, we need to analyze the given information and make deductions based on it. Let's break down the given information and solve the question step by step.

Given Information:
1. Six friends are sitting in a circle and facing the center.
2. Deepa is between Prakash and Pankaj.
3. Priti is between Mukesh and Lalit.
4. Prakash and Mukesh are opposite to each other.

Step 1: Determine the position of Prakash and Mukesh.
Since Prakash and Mukesh are opposite to each other, they must be sitting diametrically opposite in the circle.

Step 2: Determine the position of Deepa.
According to the given information, Deepa is sitting between Prakash and Pankaj. Since Prakash and Mukesh are opposite to each other, Deepa cannot be sitting next to Prakash. Therefore, Deepa must be sitting next to Pankaj.

Step 3: Determine the position of Priti and Lalit.
According to the given information, Priti is sitting between Mukesh and Lalit. Since Mukesh is sitting opposite to Prakash, Priti cannot be sitting next to Mukesh. Therefore, Priti must be sitting next to Lalit.

Step 4: Determine the position of the remaining friend.
Since all the other positions have been determined, the remaining friend must be sitting next to Prakash.

Final Answer:
Based on the deductions made, the friend sitting right to Prakash is Lalit. Therefore, option D - Lalit is the correct answer.

Directions to Solve
Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.
Question -
Who is sitting immediate right to Reeta ?
  • a)
    Bindu
  • b)
    Rani
  • c)
    Mary
  • d)
    Seema
Correct answer is option 'C'. Can you explain this answer?

Ankita Dey answered
Given Information:
- Seema is to the left of Rani and to the right of Bindu.
- Mary is to the right of Rani.
- Reeta is between Rani and Mary.

Step 1: Visualize the seating arrangement
Let's represent the seating arrangement with the following diagram:
```
[ ] [Reeta] [ ] [Mary] [Rani] [Seema]
```
We know that Reeta is between Rani and Mary. So, Reeta is sitting between Rani and Mary.

Step 2: Analyze the given information

From the given information, we can deduce the following:
1. Seema is to the left of Rani and to the right of Bindu.
- This means that Seema is sitting between Bindu and Rani.
- The seating arrangement so far: `[ ] [ ] [ ] [ ] [Rani] [Seema]`

2. Mary is to the right of Rani.
- This means that Mary is sitting to the immediate right of Rani.
- The seating arrangement so far: `[ ] [ ] [ ] [Mary] [Rani] [Seema]`

3. Reeta is between Rani and Mary.
- This means that Reeta is sitting between Rani and Mary.
- The seating arrangement so far: `[ ] [Reeta] [ ] [Mary] [Rani] [Seema]`

Step 3: Answer the question
The question asks who is sitting immediately to the right of Reeta. From the seating arrangement, we can see that Mary is sitting immediately to the right of Reeta.

Conclusion:
Therefore, Mary is sitting immediately to the right of Reeta. The correct answer is option 'C'.

A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.
The following additional facts are known.
  1. A and B are to be placed in consecutively numbered shelves in increasing order.
  2. I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.
  3. D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.
  4. K is to be placed in shelf number 16.
  5. L and J are items of the same type, while H is an item of a different type.
  6. C is a candy and is to be placed in a shelf preceded by two empty shelves.
  7. L is to be placed in a shelf preceded by exactly one empty shelf.
Which of the following statements is necessarily true?
  • a)
    All biscuits are kept before candies. 
  • b)
    There are two empty shelves between the biscuits and the candies.
  • c)
    There are at least four shelves between items B and C.
  • d)
    All candies are kept before biscuits.
Correct answer is option 'C'. Can you explain this answer?

Explanation:

Given Information:
- A and B are placed in consecutively numbered shelves in increasing order.
- I and J are placed in consecutively numbered shelves higher than A and B.
- D, E, and F are savouries and are placed in consecutively numbered shelves after all biscuits and candies.
- K is placed in shelf number 16.
- L and J are of the same type.
- H is of a different type.
- C is a candy and is placed in a shelf preceded by two empty shelves.
- L is placed in a shelf preceded by one empty shelf.

Analysis:
- From the given information, we can determine the following:
- A and B are placed in shelves 1 and 2.
- I and J are placed in shelves higher than A and B.
- D, E, and F (savouries) are placed after all biscuits and candies.
- K is placed in shelf 16.
- C is placed in a shelf preceded by two empty shelves.
- L is placed in a shelf preceded by one empty shelf.

Necessarily True Statement:
- There are at least four shelves between items B and C.
- This is true because B is placed in shelf 2, and C is placed in a shelf preceded by two empty shelves. Therefore, there are at least four shelves between B and C, making option C the correct answer.

These questions are based on the following information. P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R.
Q. If a new person U joins the group such that the initial conditions for the seating arrangement should be observed and also a new condition that U does not sit next to P, S or T be satisfied, then who will be the neighbours of P (one on either side)?
  • a)
    T and Q 
  • b)
    S and Q 
  • c)
    T and R
  • d)
    R and Q 
  • e)
    S and T
Correct answer is option 'E'. Can you explain this answer?

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

We create a new slot for the sixth person. But since U will not sit next to P, S or T, he will have to sit between R and Q. The arrangement will then look as follows:

As we can see from the diagram, the neighbours of P will be T and S.

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.
Additional Information:
1. No two persons wearing blue shirts sit on consecutively numbered chairs.
2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.
3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.
4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.
5. Persons wearing red shirts are not sitting at extreme ends.
The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".
Q. Which of the following persons is wearing a green shirt?
  • a)
    A
  • b)
    K
  • c)
  • d)
    P
Correct answer is option 'B'. Can you explain this answer?

Let the people who wear a blue, red and green shirt be denoted by b, r and g respectively. Restrictions on the seating arrangement:
1. Two b’s must not be together.
2. Three r’s must be together.
3. A ‘b’ and a ‘g’ must not be together.
4. A ‘g’ cannot sit on a chair numbered 2 or 9.
Case I: A person wearing a green shirt is sitting on chair numbered 1. It is only possible if another person wearing a green shirt sits on chair numbered 2, but this violates restriction number 4. Hence, this is also not possible.
Case II: A person wearing a blue shirt sits on chair numbered 1. The six seating arrangements that are possible are as follows.

Now, we see that the cases 4, 5 and 6 are just obtained by reversing the cases 1, 2 and 3 respectively. It can be concluded that in any possible seating arrangement, the chairs numbered 1 and 10 are always occupied by people wearing blue shirts. It is given that the number of people wearing a blue shirt is 3. Looking at the table given in the question, we observe that in each of the six arrangements two out of the three different people i.e. A, B and N always sit on chairs numbered 1 and 10.
Hence it can be concluded that the people who wear a blue shirt are A, B and N From the given table the person wearing a blue shirt can never sit on chairs numbered 2, 4, 7 and 9. So, (in arrangement I), A, B and N sitting on chairs numbered 1, 7 and 10 is inconsistent. Also, the people wearing red shirts sit on chairs numbered 2 and 9 and in all the possible arrangements five different people namely P, Q, M, Z and R are sitting on chairs numbered either 2 or 9. Therefore, P, Q, M, Z and R are wearing red shirts and K and L are wearing green shirts. K and L are wearing green shirts. Hence, K is the answer.

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.
Additional Information:
1. No two persons wearing blue shirts sit on consecutively numbered chairs.
2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.
3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.
4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.
5. Persons wearing red shirts are not sitting at extreme ends.
The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".
Q. Which of the arrangements done by Mr. Crazy is not consistent with the information stated under "Additional Information"?
  • a)
    VI
  • b)
  • c)
    III 
  • d)
    V
Correct answer is option 'B'. Can you explain this answer?

Shivam Menon answered
Let the people who wear a blue, red and green shirt be denoted by b, r and g respectively. Restrictions on the seating arrangement:
1. Two b’s must not be together.
2. Three r’s must be together.
3. A ‘b’ and a ‘g’ must not be together.
4. A ‘g’ cannot sit on a chair numbered 2 or 9.
Case I: A person wearing a green shirt is sitting on chair numbered 1. It is only possible if another person wearing a green shirt sits on chair numbered 2, but this violates restriction number 4. Hence, this is also not possible.
Case II: A person wearing a blue shirt sits on chair numbered 1. The six seating arrangements that are possible are as follows.

Now, we see that the cases 4, 5 and 6 are just obtained by reversing the cases 1, 2 and 3 respectively. It can be concluded that in any possible seating arrangement, the chairs numbered 1 and 10 are always occupied by people wearing blue shirts. It is given that the number of people wearing a blue shirt is 3. Looking at the table given in the question, we observe that in each of the six arrangements two out of the three different people i.e. A, B and N always sit on chairs numbered 1 and 10.
Hence it can be concluded that the people who wear a blue shirt are A, B and N From the given table the person wearing a blue shirt can never sit on chairs numbered 2, 4, 7 and 9. So, (in arrangement I), A, B and N sitting on chairs numbered 1, 7 and 10 is inconsistent. Also, the people wearing red shirts sit on chairs numbered 2 and 9 and in all the possible arrangements five different people namely P, Q, M, Z and R are sitting on chairs numbered either 2 or 9. Therefore, P, Q, M, Z and R are wearing red shirts and K and L are wearing green shirts. (a) I arrangement is not consistent.

Eight persons P, Q, R, S, T, U, V and W are sitting around a circular table facing the center (not necessarily in the same order). Two persons sit between Q and W. V sits immediate left of W. Three persons sit between S and T. R sits immediate left of T. U is not the neighbor of P. One person sits between P and Q.
Which of the following statement is correct?
  • a)
     Q sits to the immediate right of U.
  • b)
    One person sits between P and R.
  • c)
     Three persons sit between Q and R.
  • d)
    One person sits between S and U.
Correct answer is option 'D'. Can you explain this answer?

Eight persons: P, Q, R, S, T, U, V and W.
1) Three persons sit between S and T.
2) R sits immediate left of T.
3) One person sits between P and Q.
4) Two persons sit between Q and W.
5) V sits immediate left of W.
6) U is not the neighbor of P.
Checking o[tions one by one;
1) Q sits to the immediate right of U → False
2) One person sits between P and R → False
3) Three persons sit between Q and R → False
4) One person sits between S and U → True
Hence, option D is the correct answer.

A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.
The following additional facts are known.
  1. A and B are to be placed in consecutively numbered shelves in increasing order.
  2. I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.
  3. D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.
  4. K is to be placed in shelf number 16.
  5. L and J are items of the same type, while H is an item of a different type.
  6. C is a candy and is to be placed in a shelf preceded by two empty shelves.
  7. L is to be placed in a shelf preceded by exactly one empty shelf.
In how many different ways can the items be arranged on the shelves?
  • a)
    8
  • b)
    1
  • c)
    2
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

There are 5 types of biscuits, 3 types of candies and 4 types of savouries. Among 16 shelves, there are 4 empty shelves.
It is given that all items of same type are clustered together with no empty shelf between items of the same type.
From (3) and (4), it can be concluded that D, E, F and K are savouries.
From (2) and (5), L, I and J are of one type and H is the other type. Therefore from (6), as C is a candy, L, I J must be types of biscuits and H is a type of candy. Now using (1), we can conclude that A and B are of one type but not candies as there are only 3 types of candies.
Therefore,
Biscuits: A, B, I, J, L Candies: C, H, G Savouries: D, E, F, K
From (3), (4), (6) and (7), there shelf number 12 must be an empty shelf. Also, D, E, F and K are placed in shelves numbered 13, 14, 15 and 16 respectively.
Now from (1), (2) and (7), the sequence (from left to right) in which biscuits are kept is:
(Empty shelf), L, A, B, (I/J), (J/I).
From (6), the candies must be in the following order: (Empty shelf), (Empty shelf), C, (H/G), (G/H)
Thus, we have

 
In each case, J and I can be arranged in 2 ways and G and H can be arranged among them in 2 ways. Thus, 2 × 2 = 4 ways.
Total number of ways the items can be arranged on the shelves = 4 + 4 = 8

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