Hands of the Clock....

If the hr and minute hands of a clock are interchanged - in how many cases shall the new setup show some time?

3 Answers

62
Lokesh Verma ·

The angle of the minute hand is \theta And the hour hand is \beta

Then, \beta -\frac{\theta}{12} is a multiple of 30 degrees...

in the same way if the hands are reversed, the same logic says that, \theta-\frac{\beta}{12} is a multiple of 30

adding, we get 11\frac{\theta+\beta}{12} must be a multiple of 30...

subtracing, we get 13\frac{\theta-\beta}{12} must be a multiple of 30...

I hope you can finish this from here! (If what I have done is not with mistakes)
I am lazy right now to finish it off

1
ronak agarwal ·

yeah me too think 11

11
Devil ·

No - it's not 11.

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