Concept on Clocks

Speed of minutes hand = 360⁰ per hour = 6⁰ per minute

Speed of hours hand = 360⁰ per 12 hours = 0.5⁰ per minute

Relative speed of minutes hand over hours hand = 5.5⁰ per minute

If time is expressed as h:m, to find angle between minutes and hours hands:

At time h:0, angle between minutes and hours hands = 30h

After m minutes, ie., at h:m, minutes hand travels an angle of ‘5.5m’ relative to hours hand, and may or may not exceed the angle ‘30h’

=> the angle = 30h-5.5m (or) 5.5m-30h

If time is expressed as h:m, angle between minutes and hours hands 

= 30h-5.5m (or) 5.5m-30h