GATE Mechanical 2021 Set 2 | GA | Question: 3

Question

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 ____

• A. $\text{10.08 AM}$
• B. $\text{10.42 AM}$
• C. $\text{11.00 AM}$
• D. $\text{10.00 PM}$

Comments

Just a hint about LCM :

LCM are the smallest point where two periodic things meet.

LCM (30,32) = 480 means both of 30 and 32 are periodic and they will meet after 480 sec

Answer 1

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 is $ = 10\; \text{AM} + 8$ minutes $ = 10:08\; \text{AM}.$

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

Answer 2

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 $(A).$