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Key points to remember
A clock is divided into 60 equal minute divisions
1 minute division =
360°
60
 = 6° apart  
The clock has 12 hours numbered from 1 to 12, serially arranged.
The minute hand is twelve times faster then hour hand
In one minute, the minute hand moves one minute division = 6°
In one minute, the hour hand moves
1
2°
   
In one minute, the minute hand gains 5
1
2°
  more than hour hand  
In every hour, both the hands coincide once.
Angle traced by minute hand in 60 minutes = 360°
Angle traced by hour hand in 12 hours = 360°
In 60 minutes, the minute hand gains 55 minutes on the hour hand.
Angle between both hands
Both hands Required Angle
to be coincident 0°
to be at right angle 90°
to be in opposite direction 180°
to be in straight line 0° or 180°
 
Time of coincidence between two hands
In every hour, both the hands coincide means, they are 0 apart. Infact, if both the hands start
moving together from the same position, both the hands will coincide after
360 x 2
11
 = 65
5
11
 minutes
Note:
1. If the two hands coincide in time less than 65
5
11
 minutes, then the clock is too fast.
2. If the two hands coincide in time less more 65
5
11
 minutes, then the clock is too slow.
Incorrect clock:
An incorrect clock either gains or loses time. So, time interval indicated by such a clock will be different from that actually shown by a true clock.
Formulae:
The total time gained in T hours = T x 60
65
5
11
 - x
x
 minutes    
Where x is the time interval in which the minute hand of a clock overtakes the hour hand.
 
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