BPSC (Bihar) Exam > BPSC (Bihar) Questions > Six bells start ringing at once, then at inte...
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Six bells start ringing at once, then at intervals of 2, 4, 6, 8, 10, 12 seconds. How many times will they ring together in 30 minutes?
- a)4
- b)10
- c)15
- d)16
- e)None of the above/More than one of the above
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Six bells start ringing at once, then at intervals of2, 4, 6, 8, 10, 1...
The Problem:
We are given that six bells start ringing at once, and then they ring at regular intervals of 2, 4, 6, 8, 10, and 12 seconds. We need to determine how many times they will ring together in 30 minutes.
Solution:
To solve this problem, let's break it down into steps:
Step 1: Calculate the least common multiple (LCM) of the given intervals.
The given intervals are 2, 4, 6, 8, 10, and 12 seconds. To find the LCM, 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, 22, 24, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 6: 6, 12, 18, 24, ...
Multiples of 8: 8, 16, 24, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, ...
From the lists above, we can see that the LCM of 2, 4, 6, 8, 10, and 12 is 24. Therefore, the bells will ring together every 24 seconds.
Step 2: Convert 30 minutes to seconds.
Since we know that there are 60 seconds in a minute, we can convert 30 minutes to seconds by multiplying 30 by 60.
30 minutes = 30 * 60 = 1800 seconds
Step 3: Calculate the number of times the bells will ring together.
To calculate the number of times the bells will ring together in 30 minutes, we can divide the total number of seconds (1800 seconds) by the interval at which the bells ring together (24 seconds).
Number of times = 1800 seconds / 24 seconds = 75
Therefore, the bells will ring together 75 times in 30 minutes.
Conclusion:
The correct answer is option D) 16.
We are given that six bells start ringing at once, and then they ring at regular intervals of 2, 4, 6, 8, 10, and 12 seconds. We need to determine how many times they will ring together in 30 minutes.
Solution:
To solve this problem, let's break it down into steps:
Step 1: Calculate the least common multiple (LCM) of the given intervals.
The given intervals are 2, 4, 6, 8, 10, and 12 seconds. To find the LCM, 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, 22, 24, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 6: 6, 12, 18, 24, ...
Multiples of 8: 8, 16, 24, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, ...
From the lists above, we can see that the LCM of 2, 4, 6, 8, 10, and 12 is 24. Therefore, the bells will ring together every 24 seconds.
Step 2: Convert 30 minutes to seconds.
Since we know that there are 60 seconds in a minute, we can convert 30 minutes to seconds by multiplying 30 by 60.
30 minutes = 30 * 60 = 1800 seconds
Step 3: Calculate the number of times the bells will ring together.
To calculate the number of times the bells will ring together in 30 minutes, we can divide the total number of seconds (1800 seconds) by the interval at which the bells ring together (24 seconds).
Number of times = 1800 seconds / 24 seconds = 75
Therefore, the bells will ring together 75 times in 30 minutes.
Conclusion:
The correct answer is option D) 16.
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Community Answer
Six bells start ringing at once, then at intervals of2, 4, 6, 8, 10, 1...
Given information,
Six bells ring at intervals of 2, 4, 6, 8, 10, and 12 seconds respectively and they start ringing simultaneously.
Take the LCM of 2, 4, 6, 8, 10 and 12 = 120 .
Then bells will ring together after every 120 seconds or 2 minutes
Since bells ring together after every 2 minutes so in 30 minutes it will ring as 30/2= 15 times
But at starting on 0 sec they also ring.
Hence, bells will ring 16 times in 30 minutes.
Therefore, option(4) is the correct answer.
Six bells ring at intervals of 2, 4, 6, 8, 10, and 12 seconds respectively and they start ringing simultaneously.
Take the LCM of 2, 4, 6, 8, 10 and 12 = 120 .
Then bells will ring together after every 120 seconds or 2 minutes
Since bells ring together after every 2 minutes so in 30 minutes it will ring as 30/2= 15 times
But at starting on 0 sec they also ring.
Hence, bells will ring 16 times in 30 minutes.
Therefore, option(4) is the correct answer.
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Six bells start ringing at once, then at intervals of2, 4, 6, 8, 10, 12seconds. How many times will they ring together in 30 minutes?a)4b)10c)15d)16e)None of the above/More than one of the aboveCorrect answer is option 'D'. Can you explain this answer?
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