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Question

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes. How much in a day does the clock gain or lose?


A
Gains 56877 minutes
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B
Loses 32811 minutes
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C
Loses 910143 minutes
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D
Gains 109143 minutes
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E
Gains 1010143 minutes
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Solution

The correct option is E Gains $$\displaystyle 10 \frac{10}{143}$$ minutes

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 = $$65\dfrac { 5 }{ 11 } $$min.

But they are together after 65 min.

Therefore, gain in 65 minutes =  $$65\dfrac { 5 }{ 11 } -60=\dfrac { 5 }{ 11 } $$ min.

Gain in 24 hours = $$\dfrac { 5 }{ 11 } * \dfrac { 24*60 }{ 65 } $$ = 1440/143 min.

Therefore, the clock gains $$(10 + 10/143 )$$ minutes in $$24$$ hours.


Mathematics

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