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There are three heaps of rice weighing 120 kg, 144 kg and 204 kg. What is the maximum capacity of a bag so that the rice of each can be packed in exactly number of bags?
- a)24 kg
- b)18 kg
- c)12 kg
- d)6 kg
Correct answer is option 'C'. Can you explain this answer?
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There are three heaps of rice weighing 120 kg, 144 kg and 204 kg. What...
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There are three heaps of rice weighing 120 kg, 144 kg and 204 kg. What...
To find the maximum capacity of a bag so that the rice from each heap can be packed in an exact number of bags, we need to find the factors of each heap's weight and identify the common factors among them. The maximum capacity of the bag will be the highest common factor.
Given heaps of rice:
Heap 1: 120 kg
Heap 2: 144 kg
Heap 3: 204 kg
Finding factors of each heap's weight:
Heap 1 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Heap 2 factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Heap 3 factors: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
Identifying common factors:
Common factors of Heap 1 and Heap 2: 1, 2, 3, 4, 6, 8, 12, 24
Common factors of Heap 1 and Heap 3: 1, 2, 3, 4, 6, 12
Common factors of Heap 2 and Heap 3: 1, 2, 3, 4, 6, 12
The highest common factor among all three heaps is 12 kg. Therefore, the maximum capacity of a bag should be 12 kg so that the rice from each heap can be packed in an exact number of bags.
Hence, option C) 12 kg is the correct answer.
Given heaps of rice:
Heap 1: 120 kg
Heap 2: 144 kg
Heap 3: 204 kg
Finding factors of each heap's weight:
Heap 1 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Heap 2 factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Heap 3 factors: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
Identifying common factors:
Common factors of Heap 1 and Heap 2: 1, 2, 3, 4, 6, 8, 12, 24
Common factors of Heap 1 and Heap 3: 1, 2, 3, 4, 6, 12
Common factors of Heap 2 and Heap 3: 1, 2, 3, 4, 6, 12
The highest common factor among all three heaps is 12 kg. Therefore, the maximum capacity of a bag should be 12 kg so that the rice from each heap can be packed in an exact number of bags.
Hence, option C) 12 kg is the correct answer.
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There are three heaps of rice weighing 120 kg, 144 kg and 204 kg. What...
Answer is c
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There are three heaps of rice weighing 120 kg, 144 kg and 204 kg. What is the maximum capacity of a bag so that the rice of each can be packed in exactly number of bags?a)24 kgb)18 kgc)12 kgd)6 kgCorrect answer is option 'C'. Can you explain this answer?
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