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78 books, 114 crayons and 141 notebooks were distributed to school children equally. It was found that 6 were left undistributed in each. What was the total number of children?
- a)9
- b)8
- c)13
- d)12
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
78 books, 114 crayons and 141 notebooks were distributed to school chi...
No. of books distributed = 78 – 6 = 72
No. of crayons distributed = 114 – 6 = 108
No. of notebooks distributed = 141 – 6 = 135
As the things were distributed equally,
Total no. of children = H.C.F of 72,108,135 = 9
Most Upvoted Answer
78 books, 114 crayons and 141 notebooks were distributed to school chi...
Understanding the Problem
In this problem, we need to distribute 78 books, 114 crayons, and 141 notebooks among school children equally, with 6 items left undistributed in each category.
Step 1: Calculate the Distributed Items
- For books:
Total books = 78
Distributed books = 78 - 6 = 72
- For crayons:
Total crayons = 114
Distributed crayons = 114 - 6 = 108
- For notebooks:
Total notebooks = 141
Distributed notebooks = 141 - 6 = 135
Step 2: Find the Number of Children
Now, we need to find the number of children who received these items equally.
- Each category of items is distributed equally among the children, meaning the total number of children is a common divisor of the distributed items.
- We need to find the greatest common divisor (GCD) of 72, 108, and 135.
Step 3: Calculate the GCD
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
The common factors are 1, 3, 9.
- The GCD is 9.
Step 4: Conclusion
- The total number of children is 9, as each child receives an equal share of the items with 6 left undistributed in each category.
Hence, the correct answer is option 'A'.
In this problem, we need to distribute 78 books, 114 crayons, and 141 notebooks among school children equally, with 6 items left undistributed in each category.
Step 1: Calculate the Distributed Items
- For books:
Total books = 78
Distributed books = 78 - 6 = 72
- For crayons:
Total crayons = 114
Distributed crayons = 114 - 6 = 108
- For notebooks:
Total notebooks = 141
Distributed notebooks = 141 - 6 = 135
Step 2: Find the Number of Children
Now, we need to find the number of children who received these items equally.
- Each category of items is distributed equally among the children, meaning the total number of children is a common divisor of the distributed items.
- We need to find the greatest common divisor (GCD) of 72, 108, and 135.
Step 3: Calculate the GCD
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
The common factors are 1, 3, 9.
- The GCD is 9.
Step 4: Conclusion
- The total number of children is 9, as each child receives an equal share of the items with 6 left undistributed in each category.
Hence, the correct answer is option 'A'.
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78 books, 114 crayons and 141 notebooks were distributed to school children equally. It was found that 6 were left undistributed in each. What was the total number of children?a)9b)8c)13d)12Correct answer is option 'A'. Can you explain this answer?
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