The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?

The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?
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Answer: 32 8/11 minutes.
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A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? A.59 km/hr B.65 km/hr C.70 km/hr D.81 km/hr E. None of these

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Last Answer : In 24 hours the watch gained 1/2-1/3= 1/6 minute. It would seem it would be 5 minutes fast in 5 X 6= 30 days; that is,the morning of May 31. But already on the morning of May 28 the was 27/6 ... fast. At the close of the day the watch gained 1/2 minute more, so it was 5 minutes fast on may 28.