A 12 dial clock has its minute hand defective.Whenever it touches dial 12, it immediately falls down to 6 instead of running smoothly (the hour hand remains unaffected during that fall). It was set right at 12 '0' clock in the noon. A clock is set to show the correct time at 11 a.m. The clock gains 12 minutes in 12 hours what will be the true time when the watch indicates 1 p.m. on the 6th day ?

The watch runs fast, showing 12 hours and 12 minutes for every 12 hours of actual time, a ratio of 61 minutes shown for every 60 actual minutes. When the watch indicates 1 p.m. on the 6th day, it has been running for exactly 5 days and 2 hours, meaning 122 hours are indicated on the watch. Multiplying 122 indicated hours by the 60 divided by 61 actual time ratio yields 120 actual hours elapsed. Adding 120 hours (5 days) to the 11 a.m. start time makes the true time 11 a.m.

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