As you know, a clock is a device that measures and shows time. The clock consists of two arms called the minute hand and hour hand. (In clock problems, generally the existence of the second hand is neglected.) The dial of a clock is a circle (360^{O}) whose circumference is divided into 12 parts, called hour spaces. Each hour space is divided into 5 parts, called minute spaces. Thus, the whole circumference of the clock is divided into 12 × 5 = 60 minute spaces.

### Important facts and shortcuts for quick calculation

- In 1 hour, hour hand will cover = 30
^{o}. - In 1 minute, minute hand will cover = 6
^{o}. - For the minute hand and hour hand to coincide, the angle between them should be 0
^{o}. - During every hour, minute hand and hour hand coincide once.
- Both the hands coincide after every 65
- For the minute hand and hour hand to lie opposite to each other, the angle between them should be 180
^{o}. - In 60 minutes, the minute hand gains 55 minutes on the hour hand.
- In minutes, the minute hand gains 1 minute over the hour hand.
- To convert minutes into hours, divide the corresponding minutes by 60.
- To convert seconds into hours, divide the corresponding seconds by 3600.

### Important formulas

- Angle between H hours and M minutes = 1/2×|60H – 11M|

where, H is the time in hours, M is the time in minutes.

*Note: |x| means absolute value or modulus value of x. It simply takes the positive value of the given number. *

- To find the mirror image of any given time (except any time between 11 and 1), subtract the given value from 11:60.
- To find the mirror image of any time between 11 and 1, subtract the given value from 23:60.

*“For detailed theory, refer the book “CSIR-NET General Aptitude – A New Outlook”*