Answer:
11 109/121
Step-by-step 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