Clocks

• 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..