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A digital watch $\text{X}$ beeps every $30$ seconds while watch $\text{Y}$ beeps every $32$ seconds. They beeped together at $\text{10 AM}$.

The immediate next time that they will beep together is ____

  1. $\text{10.08 AM}$
  2. $\text{10.42 AM}$
  3. $\text{11.00 AM}$
  4. $\text{10.00 PM}$
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Given that, a digital watch $\text{X}$ beeps every $30$ seconds while watch $\text{Y}$ beeps every $32$ seconds.

Now, digital watch $X$ and $Y$ beep together every $ = \text{LCM}(30,32) = 480$ seconds $ = 8$ minutes.

First, they beeped together at $10\; \text{AM}$. Then the immediate next time that they will beep together $ = 10\; \text{AM} + 8$ minutes $ = 10:08\; \text{AM}.$

So, the correct answer is $(A).$
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