Question

The minute hand of a clock overtakes(or coincides) the hour hand at intervals of 65 minutes of correct time How much does the clock gain or lose in 12 hours?

Answer 1

In a correct clock, both the hands coincide (or overtake) at an interval of 6551165511 minutes
But, here it coincides at an interval of 65 minutes
Since 65511>6565511>65, so, the clock is gaining time
Using the formula,
Total time gained in T hours
=(T×60)(65511−x)x=(T×60)(65511−x)x minutes
Where T = 12 hours, x = 65
∴∴ Total time gained in 12 hours
=(12×60)(65511−65)65minutes.=(12×60)(65511−65)65minutes.
=12×60×511×16512×60×511×165 minutes=5514355143 minutes