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Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ?
Most Upvoted Answer
Six bells commence tolling together and toll at intervals of 2, 4, 6, ...
LCM of 2,4,6,8,10,12 = 120
So all the bells toll together after every interval of 120 minutes (once in every 2 hours)
Now 30 hours = 1800 minutes and 1800/120 = 15
So all of them toll together for a total of 15 times in 30 hours (once in every 2 hours).
Community Answer
Six bells commence tolling together and toll at intervals of 2, 4, 6, ...
Introduction:
In this problem, we are given that six bells toll at different intervals and we need to determine how many times they toll together in a span of 30 hours. To solve this problem, we will find the least common multiple (LCM) of the given intervals and then calculate the number of times they toll together using the formula LCM/interval.
Step 1: Finding the LCM of intervals:
To find the LCM of the given intervals, we can list the multiples of each interval until we find a common multiple.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 4: 4, 8, 12, 16, 20, ...
Multiples of 6: 6, 12, 18, 24, ...
Multiples of 8: 8, 16, 24, ...
Multiples of 10: 10, 20, ...
Multiples of 12: 12, 24, ...
From the above lists, we can see that the LCM of the given intervals is 24.
Step 2: Calculating the number of times they toll together:
To calculate the number of times the bells toll together in 30 hours, we need to convert the hours into minutes. Since there are 60 minutes in an hour, we have:
30 hours * 60 minutes/hour = 1800 minutes
Now, we can divide the total minutes by the LCM to get the number of times they toll together:
1800 minutes / 24 minutes = 75 times
Conclusion:
Therefore, the bells toll together 75 times in a span of 30 hours.
In this problem, we are given that six bells toll at different intervals and we need to determine how many times they toll together in a span of 30 hours. To solve this problem, we will find the least common multiple (LCM) of the given intervals and then calculate the number of times they toll together using the formula LCM/interval.
Step 1: Finding the LCM of intervals:
To find the LCM of the given intervals, we can list the multiples of each interval until we find a common multiple.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 4: 4, 8, 12, 16, 20, ...
Multiples of 6: 6, 12, 18, 24, ...
Multiples of 8: 8, 16, 24, ...
Multiples of 10: 10, 20, ...
Multiples of 12: 12, 24, ...
From the above lists, we can see that the LCM of the given intervals is 24.
Step 2: Calculating the number of times they toll together:
To calculate the number of times the bells toll together in 30 hours, we need to convert the hours into minutes. Since there are 60 minutes in an hour, we have:
30 hours * 60 minutes/hour = 1800 minutes
Now, we can divide the total minutes by the LCM to get the number of times they toll together:
1800 minutes / 24 minutes = 75 times
Conclusion:
Therefore, the bells toll together 75 times in a span of 30 hours.
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Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ?
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Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ?.
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively . In 30 hours, how many times do they toll together ?.
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