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Introduction:     A clock is a device which shows time. It consists of two hands the hour hand and the minute hand.  The hou...

# 16. Aptitude Questions -- CLOCKS - Introduction and Important Theory

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 3600
In 60 minutes the minute hand makes 3600
So in one minute the minute hand makes $\frac{360}{60}$ that is 60
Therefore each minutes space = 3600 i.e., minute spaces are 60 apart.

2.    In one hour the hour hand makes $\frac{360}{12}$ i.e., 300
In 60 minutes the hour hand makes 300
So in one minute the hour hand makes $\frac{30}{60}$ that is $\frac{1}{2}$ 0
Therefore each hour space = 300 i.e., hour spaces are 30apart.
3. The minute hand moves through 60 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 5.50  per minute.

4.  When the 2 hands are coincident, they are 00 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 (900) 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

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

For examples and solved problems on clocks  , go through Solved Problems on Clocks

For more problems and On-line tests on Quantitative aptitude, visit  http://www.9exams.com