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A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?
- a)20
- b)14
- c)42
- d)38
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A chocolate dealer has to send chocolates of three brands to a shopke...
Given Information:
- The dealer has to send chocolates of three brands: A, B, and C.
- The number of boxes to be sent are 96 of brand A, 240 of brand B, and 336 of brand C.
- All brands are packed in boxes of the same size.
- The boxes are to be packed in cartons of the same size.
- Each carton should contain boxes of the same brand of chocolates.
To find: The minimum number of cartons the dealer has to send.
Step-by-Step Solution:
1. Calculate the number of cartons for each brand:
- Number of boxes of brand A = 96
- Number of boxes in each carton for brand A = X (let's assume)
- Number of cartons for brand A = Number of boxes of brand A / Number of boxes in each carton for brand A = 96 / X
- Number of boxes of brand B = 240
- Number of boxes in each carton for brand B = X (same as brand A)
- Number of cartons for brand B = Number of boxes of brand B / Number of boxes in each carton for brand B = 240 / X
- Number of boxes of brand C = 336
- Number of boxes in each carton for brand C = X (same as brand A and B)
- Number of cartons for brand C = Number of boxes of brand C / Number of boxes in each carton for brand C = 336 / X
2. As per the given condition, each brand should be packed in cartons of the same size. Therefore, the number of cartons for each brand should be a whole number.
3. Determine the factors of the number of boxes for each brand:
- Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
- Factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
4. Find the common factors of the number of boxes for each brand.
- Common factors of 96, 240, and 336: 1, 2, 3, 4, 6, 8, 12, 16, 24
- The minimum number of cartons that can be sent is equal to the highest common factor of the number of boxes for each brand.
5. The highest common factor of 96, 240, and 336 is 24.
6. The minimum number of cartons the dealer has to send is 24.
Therefore, the correct answer is option B) 14.
- The dealer has to send chocolates of three brands: A, B, and C.
- The number of boxes to be sent are 96 of brand A, 240 of brand B, and 336 of brand C.
- All brands are packed in boxes of the same size.
- The boxes are to be packed in cartons of the same size.
- Each carton should contain boxes of the same brand of chocolates.
To find: The minimum number of cartons the dealer has to send.
Step-by-Step Solution:
1. Calculate the number of cartons for each brand:
- Number of boxes of brand A = 96
- Number of boxes in each carton for brand A = X (let's assume)
- Number of cartons for brand A = Number of boxes of brand A / Number of boxes in each carton for brand A = 96 / X
- Number of boxes of brand B = 240
- Number of boxes in each carton for brand B = X (same as brand A)
- Number of cartons for brand B = Number of boxes of brand B / Number of boxes in each carton for brand B = 240 / X
- Number of boxes of brand C = 336
- Number of boxes in each carton for brand C = X (same as brand A and B)
- Number of cartons for brand C = Number of boxes of brand C / Number of boxes in each carton for brand C = 336 / X
2. As per the given condition, each brand should be packed in cartons of the same size. Therefore, the number of cartons for each brand should be a whole number.
3. Determine the factors of the number of boxes for each brand:
- Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
- Factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
4. Find the common factors of the number of boxes for each brand.
- Common factors of 96, 240, and 336: 1, 2, 3, 4, 6, 8, 12, 16, 24
- The minimum number of cartons that can be sent is equal to the highest common factor of the number of boxes for each brand.
5. The highest common factor of 96, 240, and 336 is 24.
6. The minimum number of cartons the dealer has to send is 24.
Therefore, the correct answer is option B) 14.
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Community Answer
A chocolate dealer has to send chocolates of three brands to a shopke...
The number of boxes of brands A,B and C is 96,240 and 336 respectively. Each carton should contain boxes of the same brand and also an equal number of boxes. This can happen only when each carton contains a number of boxes that is a factor of the number of boxes of each brand i.e. a factor of 96,240 and 336. To get the minimum number of cartons, the number of boxes in each carton should be maximum. So, we should take the highest common factor of 96,240 and 336.
96=24×4,240=24×2×5 and 336=24×2×7
So, the highest common factor =24×2=48
So the number of cartons containing boxes of brand
A=96/48=2
Number of cartons containing boxes of brand
B=240/48=5
Number of cartons containing boxes of brand
C=336/48=7
∴ Total numbers of cartons =2+5+7=14
Hence, the correct option is (B).
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A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. Can you explain this answer?
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A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. 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 chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. 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 chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. Can you explain this answer?.
A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. 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 chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. 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 chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. Can you explain this answer?.
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A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size. The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C. These boxes are to be packed in cartons of the same size containing an equal number of boxes. Each carton should contain boxes of the same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?a)20b)14c)42d)38Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
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