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Question

At what time between 4 and 5 will the hands of a watch point in opposite directions?

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Solution

They will be opposite to each other when there is a space of 30 minutes between them
This will happen when the minute hand gains (30+20) minutes = 50 minutes
The minute hand gains 50 minutes in
50×6055=5461150×6055=54611 minutes
i.e., they will point in opposite directions at 5461154611 minutes
past 4.

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