The minute hand (M.H) passes over 60 minute spaces (M.S) in 1 hour.
The hour hand (H.H) goes over 5 minute spaces (M.S) in 1 hour.
The minute hand (M.H) takes 60 minutes to gain 55 minute spaces (M.S) over the hour hand (H.H).
To gain 1 M.S over the H.H., it takes 60/55 min or 12/11 min for the minute hand.
In every hour:
The hands coincide once.
The hands are straight (pointing in opposite directions) once. In this position, the hands are 30 minute spaces (M.S) apart.
The hands are twice at right angles. In this position the hands are 15-minute spaces apart.
The minute hand moves through 6 degrees in each minute whereas the hour hand moves through 1/2 DEGREES in each minute.
In a day, i.e., in 24 hours:
The hands coincide 11 times in every 12 hours (Since, between 11 and 1 o'clock, there is a common position 12 o'clock when the hands coincide. Hence 22 times in 24 hours
The hands point towards exactly opposite directions 11 times in 12 hours (between 6 and 7, there is a common position 6 o'clock, when the hands are straight). Hence 22 times in 24 hours.
The hands of a clock are at right angles twice every hour, but in 12 hours, they are at right angles 22 times and thus 44 times in a day. There are two positions common in every 12 hours, one at 3 o'clock and again at 9 o'clock.
Any relative position of the hands of a clock is repeated 11 times in every 12 hours.
The hands are straight (coincide or in opposite directions) 44 times in 48 hours..