Question

If the hands of a clock coincide every 66minutes how much does the clock gain or lose every hour

Answer 1

Answer:

11 109/121

Explanation:

The angle between 2 successive numbers in the clock is; 360/12 = 30°

The angle between successive dots is;

360/60 = 6°

For one rotation of minutes hand hours hand rotates by 30°

For increase in 1 minute there is increase of ½° for hours hand.

Net decrease for 1 min is; 11/2°

For x min the decrease must be 30°. Thus;

x = 60/11

So the hands to co incide again it takes 60 + 60/11 = 65 5/11

The clock shows 6/11 minimum error for 66 minutes.

The clock shows x min error for 24×60. Thus;

x = ((5/11) * 24 * 60)/11

x = 11 109/121