Sunday, 12 January 2014

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

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 3600
       In 60 minutes the minute hand makes 3600
       So in one minute the minute hand makes
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
360 / 12
i.e., 300
        In 60 minutes the hour hand makes 300
        So in one minute the hour hand makes
30 / 60
that is 1/20
        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           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 00 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 (900) 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.

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