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Four bells ringing together and ring at an interval of 12 sec, 15 sec, 20 sec, and 30 sec respectively. How many times will they ring together in 8 hours?  

  • a)
    481

  • b)
    480

  • c)
    482

  • d)
    483

Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Four bells ringing together and ring at an interval of 12 sec, 15 sec,...
Given:
Four bells ringing timing is 12 sec, 15 sec, 20 sec,30 sec 
Calculation:
Four bells ringing timing is 12 sec, 15 sec, 20 sec,30 sec 
Now we have to take LCM of time interval
⇒ LCM of (12, 15, 20, 30) = 60
Total seconds in 8 hours = 8 × 3600 = 28800
Number of times bell rings = 28800/60
⇒ Number of times bell rings = 480
If four bells ring together in starting
⇒ 480 + 1 
∴ The bell ringing 481 times in 8 hours.
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Most Upvoted Answer
Four bells ringing together and ring at an interval of 12 sec, 15 sec,...
To find out how many times the bells will ring together in 8 hours, we need to determine the least common multiple (LCM) of the time intervals at which they ring.

Finding the LCM:
To find the LCM of the given time intervals (12 sec, 15 sec, 20 sec, and 30 sec), we can list the multiples of each number until we find a common multiple.

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, ...

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, ...

Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, ...

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, ...

The smallest common multiple we can find from these lists is 60. Therefore, the bells will ring together every 60 seconds or 1 minute.

Calculating the number of times they will ring together in 8 hours:
There are 60 minutes in an hour and 8 hours in total. So, the total number of minutes is 60 * 8 = 480 minutes.

Since the bells will ring together every 1 minute, they will ring together 480 times in 8 hours.

Therefore, the correct answer is option 'A', 481 times.
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Directions for Questions: Answer the questions on the basis of the information given below.From ISBT, buses ply on 6 different routes viz. 414, 413, 427, 966, 893 and 181 at an interval of 10 min, 10 min, 12 min, 15 min, 20 min and 30 min, not necessarily in that order, to four different destinations viz. Mehrauli, Badarpur, Uttam Nagar and Azadpur. There is at least one bus for each destination. Further information is also known:i. Two buses to the same destination cannot start at the same time.ii. If the timings of two buses plying different routes but heading towards the same destination clash, then the bus of the route number having the shorter time interval will skip this journey.iii. Buses on two different routes ply between ISBT and Mehrauli.iv. The difference between the time intervals of a route to Mehrauli and Uttam Nagar is equal to the difference between the time intervals of the two routes to Uttam Nagar.v. Buses on a route to Mehrauli leaves after every 10 min.vi. 414 leaves for Badarpur after every 30 min.vii. Time intervals between two different routes heading towards the same destination cannot be equal.viii. Buses on one of the routes to Uttam Nagar leave after every 15 min.ix. Buses to any destination can leave from ISBT with an interval of at least one minute or an integral multiple of one minute.(2015)Q.Which of the following statements is necessarily TRUE?

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Four bells ringing together and ring at an interval of 12 sec, 15 sec, 20 sec, and 30 sec respectively. How many times will they ring together in 8 hours?a)481b)480c)482d)483Correct answer is option 'A'. Can you explain this answer?
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