__Introduction:__

A clock is a device which
shows time.

It consists of two hands
the hour hand and the minute hand.

The hour hand (short hand)
indicates time in hours and the minute hand or long hand indicates time in
minutes.

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 moves
5 minute spaces. While the minute hand movess 60 minute spaces

Therefore 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 $\frac{360}{60}$
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 $\frac{360}{12}$ i.e., 30

^{0}

In 60 minutes the hour hand makes 30

^{0}
So in one minute the hour hand makes
$\frac{30}{60}$
that is $\frac{1}{2}$

^{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 $\frac{1}{2}$

^{0}in each minute.

Thus in one minute the minute hand gains 5
½

^{0}than the hour hand.
Relative speed of the
minute hand and the hour hand is 5.5

^{0}per minute.

**4.**

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

^{0}are 0 minutes apart.

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

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

iii)In 24 hours the two hands coincide 22
times

**5.**When the 2 hand are in opposite direction they are $\frac{180}{6}$ i.e., 30 minutes apart.

**i)**It happens only once in an hour.

**ii)**In one 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 position 6’ O clock
between 5 O’ clock and 11’ O clock.

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

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

^{0}) or 15 minutes spaces apart.

i) It happens 2
times in one hour.

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

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

**7.**The minute and hour hands of a clock coincide for every 65$ \frac{5}{11}$ minutes.

__Too Fast:__

When the clock indicates
time more than 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.

If the two hands of a
clock meet each other in less than 65 $ \frac{5}{11}$
minutes, the clock is said to be running fast

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.

If the two hands of a
clock meet each other in more than 65 $ \frac{5}{11}$
minutes, the clock is said to be running fast

For example, the clock
indicates 9:30 am when the correct time is 9:45 am it is set to be 15 minutes
slow

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

__Note :__
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