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 $12 : 00$ $\text{PM}$, when will the three bells ring together again the next time?

1. $5 : 00$ $\text{PM}$
2. $5 : 30$ $\text{PM}$
3. $6 : 00$ $\text{PM}$
4. $6 : 30$ $\text{PM}$

Given that,

• $\text{P}$ is rung every $20$ minutes
• $\text{Q}$ is rung every $30$ minutes
• $\text{R}$ is rung every $50$ minutes

Now, ${\color{Green}{\text{LCM(50, 30, 50) = 300 minutes = 5 hours}}.}$

If all the three bells are rung at $12: 00\;\text{PM}$, when will after that all the three bells ring together again the next time $= 12:00\;\text{PM} + 5\;\text{hours} = 5:00\;\text{PM}.$

Correct Answer $:\text{A}$

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