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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?  

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?   Correct Answer 5:00 PM

Given:

P bell is rung every 20 minutes.

Q bell is rung every 30 minutes.

R bell is rung every 50 minutes.

All of the three bells are rung at 12:00 PM.

Concept used:

We have to find the LCM of 20, 30, and 50 to find the time which after all three bells will ring together.

Formula used:

1 minute = 1/60 hour

Calculation:

Prime factors of 20 = 2 × 2 × 5

Prime factors of 30 = 2 × 3 × 5

Prime factors of 50 = 2 × 5 × 5

LCM of 20, 30, and 50 = 2 × 2 × 3 × 5 × 5 = 300

∴ All three bells will ring together after 300 minutes.

300 minutes = 300/60 h = 5 hours

∴ All three bells will ring together at (12:00 PM + 5 hours) = 5:00 PM

∴ If all the three bells are rung at 12:00 PM, the three bells will ring together again at 5:00 PM.

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