Multiple choice

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 -

  1. $75^o$
  2. $60^o$
  3. $90^o$
  4. $105^o$
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A Correct answer
Explanation

At 3:30, the hour hand is halfway between 3 and 4 (15 degrees past 3). The minute hand, due to the defect, is at 6 (180 degrees from 12). The angle between 3 and 6 is 90 degrees. Subtracting the 15 degrees the hour hand moved, we get 75 degrees.

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