Clocks is very important topic in Quantitative Aptitude .It is very easy ,if once you understand the concept .Time Saving Shortcuts are also included

1. CLOCKS
Clocks is very important tool to check
whether we are doing the given task
at particular time, or in time.
Questions on clocks are very
common in the competitive exams
,aptitude based exams – CSAT,CAT
placements,GRE,GATE,etc.

2. Questions are normally based on the
1. Angle between the two hands of
the clock.
2. Time between the given angle.
3. Gain/Loss in time problems.

3. • Clocks shows 12 hours on its face or
dial.
It has two hands mainly – the
smaller one :hour hand, larger one -
minute hand.
Hand takes 12 hours to complete
one full rotation.
Minute hand takes 1 hour to
complete one full rotation.

4. • Face of clock is divided into 60
divisions.
 Minute hand :
1 hour = 360 degree.
1 minute = 6 degree.
 Hour hand :
12 hours =360 degree.
1 hour = 30 degree.
1 minute = 0.5 degree.

5. • Rate of change of angles in degrees
per minute.
From the previous slide data, we
have
Rate of change of angle of minute
hand = 12 times the rate of change
of angle of hour hand.

6. Some points to remember
TSRs
• In 60 minutes, the minute hand
gains 55 minutes on the hour hand.
• In every hour, both the hands
coincide once.
• Hands are in same straight line,
when they are coincident or opposite
each other.
• When the two hands are at right
angles , they are 15 minutes apart.

7. • Angles made by the hour hand at
H:M am/pm
= (60H+M)/2
• Angle made by the minute hand at
H:M am/pm
= 6M
• Hour hand & minute hand meet each
other after every 65.45 minutes ( or
37.72 degrees).

8. • At “X ‘o clock “ , the angle of hour
hand from the vertical is 30X degrees.
• Hour hand & minute hand are in
opposite direction (180 degree) – 11
times in 12 hours & 12 hours in 24
hours.
• Hour & minute hands are at any other
angle - 22 times in 12 hours & 44
times per day.

9. • Mirror clock :
when the time in the clock is known
, what will it be shown , when it is
seen in mirror (time) or vice versa.
If the shown is 4:20 , then what time
will be shown in the mirror clock?
Just subtract it from 12:00
We get , ( 11-4) : (60-20)
>> 7 : 40

10. Gap between two meetings of
the hour hand & minute hand
• Gap between two meetings of the hour
hand & minute hand
= 12 hours / 11
or
= 720 minutes/11
or
=65.45 minutes
or
= 1 hour 5 minutes 45 seconds

11. Q. Find the time at which the hands of
clock meet / overlap
a) 3 and 4’ o clock
1 : 05 : 5/11
Multiply the above given by the
first timing given.
we get 3: 15 :15/11
we get convert 15/11 to 1:4/11
Therefore , we get
3:16: 4/11 is the time when the two hands
of clock meet/overlap.

12. Q. Find the time at which the hands of
clock meet / overlap
b ) 6 and 7’ o clock
1 : 05 : 5/11
Multiply the above given by the
first timing given.
we get 6: 30 :30/11
we get convert 30/11 to 2 : 8/11
Therefore , we get
6:32: 8/11 is the time when the two hands
of clock meet/overlap.

13. Q. Find the time at which the hands of
clock meet / overlap
a) 7 and 8’ o clock
1 : 05 : 5/11
Multiply the above given by the
first timing given.
we get 7: 35 :35/11
we get convert 35/11 to 3:2/11
Therefore , we get
7:38: 2/11 is the time when the two hands
of clock meet/overlap.

14. Q. Find the time at which the hands of
clock meet / overlap
a) 3:30 and 4:30
1 : 05 : 5/11
Multiply the above given by the
second timing given ( as it is of different kind ).
we get 4: 20 :20/11
we get convert 20/11 to 1:9/11
Therefore , we get
4:21: 9/11 is the time when the two hands
of clock meet/overlap.