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Question

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 'O' clock in the noon.
At the time half past three, the angle between hour and minute hands of the watch will be -

A
75o
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B
60o
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C
90o
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D
105o
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Solution

The correct option is C 75o
The answer is option A
Speed of an hour hand =360(12×60)=0.5o/hr

At 3'O clock, the minute had would've fallen down to 6 and the hour hand would be in 3
In 30 mins, the minute hand would again move to 12 and fall down to 6
The distance covered by the hour hand in this 30 mins =30×0.5=15o
The hour hand has moved 15o from the number 3 on the clock, while the minute hand is on number 6 on the clock at 3:30
Angle between the hour and minute hand =9015=75o


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