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If two incorrect watches are set at 12:00 noon at correct time, when will both watches show the correct time for the first time given that the first watch gains 1 min in one hour and second watch looses 4 min in two hours.

If two incorrect watches are set at 12:00 noon at correct time, when will both watches show the correct time for the first time given that the first watch gains 1 min in one hour and second watch looses 4 min in two hours. Correct Answer 12 noon, 30 days later

First watch:It shows correct time when it creates difference of 12 hours.So, to create difference of 12 hour, time required = $$\frac{{60 \times 12}}{{24}}$$   = 30 days
Second watch:It shows correct time when it creates difference of 12 hours.So, to create difference of 12 hour, time required = $$\frac{{30 \times 12}}{{24}}$$   = 15 daysNow, LCM of 30 and 15 gives the time when they show correct time together. Thus, required time = 30 days, at same time.

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