The document discusses concepts related to clocks, including: - Clock dials are divided into 12 hour spaces, with each hour space further divided into 5 minute spaces. - In 60 minutes, the minute hand gains 55 minutes on the hour hand. - Key points about the relationship between the hour and minute hands at different times, such as being coincident once per hour or at a 90 degree angle twice per hour. - A formula is provided to calculate the angle between the hands based on the number of hours and minutes.

1. PAWAN MISHRA
APTITUDE TRAINER
mishrapawan082@gmail.com

2. Many of times questions appear on clocks in
certain exams. here, we discuss some
concept related to clocks covering all type
of questions asked.

3. The dial of clock is a circle whose
circumference is divided into 12 equal part,
called hour space. Each hour space are
further divided into 5 parts, called minute
space . This way, the whole circumference
is divided into 12*5 = 60 minute spaces.

4. The time taken by the hour hand (smaller hand)
to cover a distance of an hour space is equal
to the time taken by the minute hand (longer
hand) to cover a distance of the whole
circumference. Thus, we may conclude that
in 60 minutes, the minute hand gains 55
minutes on the hour hand.
Note : The above statement (underlined) is very much useful in solving the
problems in this chapter, so it should be remembered. The above statement
wants to say that :

5. “ In an hour, the hour-hand moves a
distance of 5 minute spaces whereas the
minute-hand a distance of 60 minute
spaces. Thus the minute-hand remains 60
- 5 = 55 minute spaces ahead of the hour-
hand.”

6. 1. In every hour, both the hands coincide once.
2. When the two hands are at right angle, they
are 15 minute spaces apart. This happens
twice in every hour.
3. When the hands are in opposite directions,
they are 30 minute spaces apart. This
happens once in every hour.

7. 4. The hands are in the same straight line when
they are coincident or opposite to each other.
5. The hour hand moves around the whole
circumference of clock once in 12 hours. So
the minute hand is twelve times faster than
hour hand.
6. The clock is divided into 60 equal minute
divisions.

8. 7. 1 minute division = = = apart
8. The clock has 12 hours numbered from 1
to 12 serially arranged.
9. Each hour number evenly and equally
separated by five minute divisions = (5×
) = apart.

9. 10. In one minute, the minute hand moves
one minute division or .
11. In one minute, the hour hand moves
12. In one minute the minute hand
gains more than hour hand.

10. 13. When the hands are together, they
are apart. Hence,
Formed in
12 hours
Formed in
24 hours
11 22
22 44
θ

11. In a correct clock the hands of a clock
coincide in every .
If the hands of a clock coincide in less than
then clocks gains time and if the
hands of a clock coincide in more than
then the clock looses time.

12. If a watch indicates 9.20, when the correct
time is 9.10, it is said to be 10 minutes too
fast. And if is said to be 10 minutes too
fast. And if it indicates 9.00, when the
correct time is 9.10, it is said to be 10
minutes too slow.

13. It is evident that the two hand of a clock will
subtend an θ between them. At any time,
the same can be found out using the
following formula:
here m= minutes and h= hours

27. 11. The inhabitants of planet Rahu measure
time in hours and minutes which are different
from the hours and minutes of our
earth. Their day consists of 36 hours with
each hour having 120 minutes. The dials of
their clocks show 36 hours. What is the angle
between the hour hand and the minutes hand
of a Rahuian clock when it shows a time of
9:48? [Rahuians measure angles in degrees
the way we do on earth. But for them, the
angle around a point is 720 degrees instead
of 360 degrees. ]