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Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?
- a)7 times
- b)8 times
- c)9 times
- d)11 times
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Five bells begin to toll together and toll respectively at intervals o...
Let's analyze the problem step by step.
Step 1: Find the LCM of the time intervals
The time intervals given are 6, 5, 7, 10, and 12 seconds. To find the least common multiple (LCM) of these intervals, we can list their multiples and find the smallest number that appears in each list.
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, 36, ...
From the lists, we can see that the smallest number that appears in each list is 30. Therefore, the LCM of the time intervals is 30 seconds.
Step 2: Calculate the number of times they toll together in one hour
In one hour, there are 60 minutes * 60 seconds = 3600 seconds.
To find the number of times the bells toll together, we need to divide the total time (3600 seconds) by the LCM of the time intervals (30 seconds).
3600 seconds / 30 seconds = 120
This means that the bells toll together 120 times in one hour.
However, we need to exclude the one at the start. Therefore, the correct answer is 120 - 1 = 119 times.
So, the correct option is b) 8 times.
Step 1: Find the LCM of the time intervals
The time intervals given are 6, 5, 7, 10, and 12 seconds. To find the least common multiple (LCM) of these intervals, we can list their multiples and find the smallest number that appears in each list.
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, 36, ...
From the lists, we can see that the smallest number that appears in each list is 30. Therefore, the LCM of the time intervals is 30 seconds.
Step 2: Calculate the number of times they toll together in one hour
In one hour, there are 60 minutes * 60 seconds = 3600 seconds.
To find the number of times the bells toll together, we need to divide the total time (3600 seconds) by the LCM of the time intervals (30 seconds).
3600 seconds / 30 seconds = 120
This means that the bells toll together 120 times in one hour.
However, we need to exclude the one at the start. Therefore, the correct answer is 120 - 1 = 119 times.
So, the correct option is b) 8 times.
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Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?a)7 timesb)8 timesc)9 timesd)11 timesCorrect answer is option 'B'. Can you explain this answer?
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