SOLUTION: a clock loses 1 second every minute. It is set to the correct time at 10 AM on February 4. In which month is the next day on which it shows the correct time? (Note: a person can

That will be when it has lost exactly 24 hours. 

24 hours = 24×60 minutes = 1440 minutes = 1440×60 seconds = 86400 seconds

So at the rate of losing 1 second every minute, it will take it
86400 minutes to lose 24 hours.

86400 minutes =  hours = 1440 hours =  days = 60 days.

Edwin

60 days is correct.  And the month is April.

However you could work it much easier this way this way:

Since it loses 1 second every 60 seconds,

it loses 1 whole day every 60 days.

Edwin