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Three bells P, Q and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes.If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?
  • a)
    5:00 PM
  • b)
    5:30 PM
  • c)
    6:00 PM
  • d)
    6:30 PM
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Three bells P, Q and R are rung periodically in a school. P is rung ev...
Solution:

To find the time when all three bells will ring together again, we need to find the least common multiple (LCM) of the time intervals of each bell.

The time intervals of the three bells are:

- P: 20 minutes
- Q: 30 minutes
- R: 50 minutes

Finding the LCM of these time intervals:

- Prime factorize each number:

- 20 = 2^2 × 5
- 30 = 2 × 3 × 5
- 50 = 2 × 5^2

- Write down the highest power of each prime factor:

- 2^2 × 3 × 5^2 = 300

Therefore, the three bells will ring together again after every 300 minutes, which is 5 hours.

Starting from 12:00 PM, the next time all three bells will ring together will be:

12:00 PM + 5 hours = 5:00 PM (Option A)

Therefore, the correct answer is option A, 5:00 PM.
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Three bells P, Q and R are rung periodically in a school. P is rung ev...
Three bells P, Q, R.
P = 20 minutes Q = 30 minutes R = 50 minutes L.C.M. of 20, 30, 50 = 300 minutes = 5 hours 12:00 PM + 5 hours = 5:00 PM.
So, three bells ring together again at 5:00 P.M.
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Three bells P, Q and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes.If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?a)5:00 PMb)5:30 PMc)6:00 PMd)6:30 PMCorrect answer is option 'A'. Can you explain this answer?
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