__Introduction:__

A clock is a
devise which shows time in consists of two hands the hour hand and the minute
hand. The hour hand (short hand) indicates time in hours and the minute
had or long hand indicates time in minutes. For simplicity we will not consider
the third hand – the second hand which is also presenting many clocks and
watches.

Usually clocks
are circular in shape but we can see many other different shapes also.
Irrespective of the shape of the dial of the clocks, the minute hand and hour
hand always rotate in circular direction.

The
circumference of a dial clock is divided into 12 equal parts called hour
spaces.

Each hour
space is further subdivided into 5 equal parts called minute spaces.

Thus the
complete circumference of a dial of a clock is divided into 12 X 5 = 60 minute
spaces.

In an hour the
hour hand crosses 5 minute spaces. While the minute hand crosses 60 minute
spaces therefore is obvious that in 60 minutes, the minute hand gains(60-5=55)
minute spaces or minutes over the hour hand. This is very important and useful
conclusion and therefore should be remembered while solving the problems on
clocks.

**Some important facts:**

**1 .**In one hour the minute hand makes 360

^{0}

In 60 minutes the minute hand makes 360

^{0}
So in one minute the minute hand makes

360
60

that is 6^{0}
Therefore each minutes space = 360

^{0}i.e., minute spaces are 6^{0}apart.**2.**In one hour the hour hand makes

360
12

i.e., 30^{0}

In 60 minutes the hour hand makes 30

^{0}
So in one minute the hour
hand makes

30
60

that is 1/2^{0}
Therefore each hour space = 30

^{0}i.e., hour spaces are 30^{0 }apart.**3.**The minute hand moves through 6

^{0 }in each minute whereas the hour hand moves through 1/2

^{0}in each minute.

Thus in one minute the minute hand gains 5
½

^{0}than the hour hand.

**4.**

**When the 2 hands are coincident, they are at 0**

^{0}are 0 minutes apart.

i) In every hour
the hour hand and minute hand coincide only once.

ii) In twelve hours
the 2 hands coincide 11 times. Because there is common a position 12’O clock between 11 and 1’ O clock.

iii)
In 24 hours
the 2 hands coincide 22 times

**5.**When the 2 hand are in opposite direction they are 180/6 i.e., 30 minutes apart.

i)
It happens
only once in an hour.

ii)
In every hour
the hour hand and minute hand are in opposite direction only once.

iii)
In 12 hours
the 2 hands are in opposite direction 11 times. Because there is common a position 6’ O clock between 5 and 11’ O clock.

iv)
In 24 hours
the 2 hands opposite direction 22 times.

**6.**When the 2 hands at right angle (90

^{0}) or15 minutes spaces apart.

i) It happens 2 times in every hour.

ii) In 12 hours the hands are at right angle only
22 times. It is so because there are 2 common positions in every
12 hours i.e.,3’O clock & 9’O Clock.

iii)
In 24 hours
the 2 hands at right angle 44 times.

**7.**The minute and hour hands of a clock coincide for every 65

5
11

minutes.**Too Fast:**

When the clock
indicates time more then the correct time it is said to be running too
fast by the difference between the correct time and the time indicated by the
clock. For example, the clock indicates 9:30 am when the correct time is
9:15 am it is set to be 15 minutes fast

**Too slow:**

When the clock
indicates time less than the correct time it is said to be running too
slow by the difference between the correct time and the time indicated by the
clock. For example, the clock indicates 9:30 am when the correct time is
9:45 am it is set to be 15 minutes slow

**Note :**The minute hand moves 12 times as fast as the hour hand.

Note : The clock has two hands—the hour hand and the minute . The
hour hand (or short hand) indicates time in hours and the minute hand (or long
hand) indicates time in minutes. In an hour, the hour hand covers 5 minute
spaces while the minute hand covers 60 minute spaces. Thus, in one hour or 60
minutes, the minute hand gains 55 minute spaces over the hour hand.

This is very important and useful conclusion .It must be always
remembered while solving problems on clocks.

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