The minute hand of a clock overtakes the hours hand at intervals of 65 min of the correct time How m...........

Logical Reasoning(Master ) Clock

The minute hand of a clock overtakes the hours hand at intervals of 65 min of the correct time. How much of the day does the clock gain or lose?

the clock gains 10 10/43 minutes

the clock gains 11 10/43 minutes

the clock gains 9 10/43 minutes

the clock gains 8 10/43 minutes

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Explanation:

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.

To be together again, the minute hand must gain 60 minutes over the hour hand.
• 55 minutes are gained in 60 min.
• 60 min. are gained in [(60/55) * 60] min = 65 5/11 min.
• But they are together after 65 min.
• Therefore, gain in 65 minutes = (65 5/11 - 65) = 5/11 min.
• Gain in 24 hours = [(5/11) * (60*24)/65] = 10 10/43 min.
• Therefore, the clock gains 10 10/43 minutes in 24 hours.

Hence, option 1 is the correct answer.