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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.
Q. In how many different ways can the items be arranged on the shelves?
  • a)
    8
  • b)
    4
  • c)
    2
  • d)
    1
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A supermarket has to place 12 items (coded A to L) in shelves numbere...
The total number of biscuits = 5, the total number of candies =3 and the total number of savouries = 12-(3+5)=4 Representing the candies as C, biscuits as B and savories as S. K is to be placed in shelf number 16. D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies. Since there is no empty shelf between the items of same type, D,E,F and K are savouries and placed at 13,14,15 and 16 respectively. This can be tabulated as follows
The shelf 12 will be empty.
It is given that items are to be placed such that all items of same type are clustered together.
From 1, A and B are to be placed in consecutively numbered shelves in increasing order.
From 6, C is a candy and is to be placed in a shelf preceded by two empty shelves and from 7, L is to be placed in a shelf preceded by exactly one empty shelf.
Hence C and L are items of different types. Since C is a candy, L will be a biscuit.
From 5, L and J are items of the same type, while H is an item of a different type.
Since I and J are clustered together, I, J and L are biscuits and H is a candy.
So C,H are candies and I,J,L are biscuits. It is given that A, B are place consecutively. Hence A and B are items of same types. So A, B should be biscuits because if they are candies, there will be 4 candies.
Hence, I,J,L,A,B are biscuits and C,H and G are candies.
Now there are two empty shelves before C and exactly one empty shelf before L, then the different cases can be tabulated as follows: 
Case 1:
Case 2:
The number of arrangements for the first case = 2*2=4 
The number of arrangements for the second case = 2*2=4 
The total number of arrangements = 4+4=8
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Most Upvoted Answer
A supermarket has to place 12 items (coded A to L) in shelves numbere...
Understanding the Problem
- The problem requires arranging 12 items (coded A to L) in shelves numbered 1 to 16 according to certain conditions.
- The items include biscuits, candies, and savouries, with specific instructions on how they should be placed.
- Various constraints and relationships are provided to help determine the arrangement.

Key Observations
1. A and B are placed in consecutively numbered shelves in increasing order.
2. I and J are placed in shelves higher than those of A and B.
3. D, E, and F are savouries and come after all biscuits and candies in consecutive shelves.
4. K is placed in shelf 16.
5. L and J are of the same type, while H is of a different type.
6. C, a candy, is preceded by two empty shelves.
7. L is preceded by exactly one empty shelf.

Solution
- Based on the given conditions and relationships, we can deduce the following arrangement:
- Shelves 1 and 2: A and B (biscuits)
- Shelves 3, 4, and 5: D, E, F (savouries)
- Shelves 6 and 7: C (candy)
- Shelves 8 and 9: H (different type)
- Shelves 10 and 11: I and J (same type)
- Shelf 12: empty
- Shelf 13: empty
- Shelf 14: G (biscuit)
- Shelf 15: empty
- Shelf 16: K (savoury)
- There is only one possible way to arrange the items according to the given conditions, resulting in 8 different arrangements in total.
Therefore, the correct answer is 8 ways in which the items can be arranged on the shelves.
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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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer?
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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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer?.
Solutions for 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice 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.Q. In how many different ways can the items be arranged on the shelves?a) 8b) 4c) 2d) 1Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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