Question:
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?
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?
If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?
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To find when periodic events will coincide again, calculate the least common multiple (LCM) of the given intervals.
Updated On: Nov 27, 2025
- 5:00 PM
- 5:30 PM
- 6:00 PM
- 6:30 PM
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The Correct Option is A
Solution and Explanation
To find when all three bells will ring together again, we need to calculate the least common multiple (LCM) of their ringing intervals. The intervals are:
- P rings every 20 minutes
- Q rings every 30 minutes
- R rings every 50 minutes
The LCM of 20, 30, and 50 is calculated as follows:
\[ \text{LCM}(20, 30, 50) = 2^2 \times 3 \times 5^2 = 300 \text{ minutes}. \]
300 minutes is equal to 5 hours. Since the bells ring together at 12:00 PM, adding 5 hours to this time gives us 5:00 PM.
Thus, the three bells will ring together again at 5:00 PM.
- P rings every 20 minutes
- Q rings every 30 minutes
- R rings every 50 minutes
The LCM of 20, 30, and 50 is calculated as follows:
\[ \text{LCM}(20, 30, 50) = 2^2 \times 3 \times 5^2 = 300 \text{ minutes}. \]
300 minutes is equal to 5 hours. Since the bells ring together at 12:00 PM, adding 5 hours to this time gives us 5:00 PM.
Thus, the three bells will ring together again at 5:00 PM.
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