There are three watches, out of which one loses 1 sec every minute and one gains 1 sec every minute. All the watches are set at 10 a.m. and an alarm is activated so that each watch beeps for 1 sec after completing 1 minute. The three watches beep together when set at 10 a.m. at the beginning. At what time will they beep together again?

If the watches are set to beep every minute of real time, they will physically beep together every 60 real minutes regardless of mechanical gaining or losing. Therefore, exactly one hour after the initial 10 a.m. synchronization, all three watches will complete their real-time 60-second cycle and beep together again at 11:00 a.m.

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