CLOCK
CLOCK
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CLOCK
CLOCK
Introduction:-
The shape of a clock is generally circular
shaped & is divided in to 12 equal parts.
According to angle wise the circle consists of
360 degree. So angle wise a clock is 360
degree & each part is 30 degree. The
circumference of a clock is divided in to 60
equal spaces so each part is 5 minute
spaces.
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CLOCK
CLOCK
In one hour, when the minute hand of clock
moves around the whole circumference
which is 60 minute spaces, the hour hand
moves 5 minute spaces. As they move in the
same direction, the minute hand gains 55
minute spaces over the hour hand in 60
minutes. So that, the minute hand gains 11
minute spaces in 12 minutes.
So from the above one ,
the minute hand gains 1 minute space over
the hour hand in 1+1/11 minutes.
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CLOCK
SOME IMPORTANT POINTS:
(i) In 1 minute when the minute hand moves 6 degrees, the hour
hand moves 1/2 degree. (As 360 degree of the circle is divided
in to 60 minutes.)
Thus, in 1 minute the minute hand gains 5+1/2 degrees.
(ii) In every hour, both the hands coincide once. In 12 hour they
coincide 11 times & in a day 22 times since there is a common
position at 12 o'clock.
(iii) The hands of a clock are at right angles twice in every hour,
but in 12 hours they are at right angles 22 times & in a day 44
times since there are two common positions in every 12 hours.
In these positions the hands are 15 minute spaces apart.
(iv The hands of a clock are opposite in directions once in every
hour& in these position, the hands are 30 minutes apart.
(v) If both the hands start moving together from the same position,
both the hands will coincide after 65+5/11 minutes.
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CLOCK
Too Fast And Too Slow:
If a watch indicates 9.20, when the correct
time is 9.10, it 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.
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EXAMPLE:
CLOCK
At what time between 4 and 5 o’clock are the
hands of the clock together?
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CLOCK
Solution:
At 4 o’clock, the hour hand is at 4 and the minute
hand is at 12. It means that they are 20 min spaces
apart. To be together, the minute hand must gain
20 minutes over the hour hand. Now, we know that
55 min. are gained in 60 min.
Therefore, 20 min are gained in (60/55)*20 =240/11
=21(9/11) min.
Therefore, the hands will be together at 21(9/11)
min past 4.
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CLOCK
Question - 1
At what time between 3 & 4 o'clock will the
hands of a clock are 5 minutes apart?
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CLOCK
Solution:
At 3 o'clock, the hands are 15 minutes apart. In this
case there are two cases to be 5 minutes apart.
Case: I
when the minute hand is 5 minutes behind the
hour hand.
In this case, the minute hand has to gain 10
minutes spaces in 10+10/11 minutes.
So the time is 10 (10/11) minutes past 3 o’clock.
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CLOCK
Case ii:
When the minute hand is 5 minutes ahead of the
hour hand.
In this case the minute hand has to gain 15+5 i.e.20
minutes in 20+20/11 minutes i.e.21 9/11 minutes.
So the time is 21 9/11 minutes past 3 o’clock.
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Question - 2
CLOCK
At what time between 4 & 5 o’clock will the hands
of a clock are at right angle?
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CLOCK
Solution:
At 4 o’clock both the hands are 20 minutes apart.
When they are at right angle they are 15minutes
apart & this is possible in two cases.
Case i: When the minute hand is 15 minutes behind the
hour hand.
In this case the minute hand has to gain 5 minutes
spaces which are possible in 5+5/11 minutes.
So the time is 5 5/11minutes past 4 o’clock.
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CLOCK
Case ii: When the minute hand is 15 minutes ahead
of the hour hand.
In this case the minute hand has to gain 20+15 =35
minutes spaces in 35+35/11 minutes.
So the time is 38(2/11) minutes past 4 o'clock
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CLOCK
Question - 3
At what time between 4 & 5 o’clock will the
hands of a clock are in opposite direction?
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CLOCK
Solution:At 4 o’clock both the hands are 20 minutes
apart .But when they are opposite in
direction they are 30 minutes apart. In this
case the minute hand has to gain 20+30=50
minutes spaces. (As hands can not move in
anti clock wise)
So the minute hand can gain these 50
minutes in 50+50/11 minutes.
There fore at 54 6/11minutes past 4 o’clock
they are in opposite in direction.
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CLOCK
Question - 4
A watch, which gains uniformly, is 2
minutes slow at noon on Sunday, and is 4
minutes 48 seconds fast at 2 p.m. on the
following Sunday. When was it correct?
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CLOCK
Solution:According to the question, the watch gains
2minutes+4 minutes 48 seconds i.e.6 4/5 minutes
or 34/5 minutes in170 hour. (As the duration of the
time from 12 noon on Sunday to2 p.m. on the
following Sunday is 170 hours)
The watch was correct when it gains the slow time
of 2 minutes. So the watch gains these 2 minutes
slow in 2*5/34*170 i.e. in 50 hours.
These 50 hours =2 days& 2 hours. So the watch
was correct after 2 days 2 hours from Sunday
noon, i.e. at 2 p.m. on Tuesday.
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CLOCK
Question - 5
A watch, which gains 5 seconds every 3 minutes,
is set right at 6 a.m. What is the true time in the
afternoon of the same day when the watch
indicates a quarter past 3?
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CLOCK
Solution:According to the wrong clock, when the time is 3
minutes 5 seconds it is 3 minutes on the correct
clock.
The wrong clock, in 3 minutes 5 seconds gains
5seconds. So in 9 hours 15 minutes, it gains 15
minutes. (As from 6 a.m. to quarter past 3, the
duration is 9 hours 15 minutes)
Hence the true time is 15 minutes behind 15
minutes past 3 i.e. 3 p.m.
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CLOCK
Question - 6
How much time does a clock gain or loses
per day if its hands coincide every 66
minutes?
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CLOCK
Solution:In correct clock both hands coincide at an interval
of 65 5/11 minutes. So in this case, in 66 minutes
the clock loses 6/11 minutes...
In 1 hour or 60 minutes the clock lose
( 6/11)*(1/66)*60 minutes.
So in a day in 24 hours the clock lose
6/11*1/66*60*24=1440/121 minutes.
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Question - 7
CLOCK
A clock loses 5 seconds an hour and is set right
Sunday at noon. What time will it indicate on the
following Monday at noon?
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Database structure
CLOCK
Solution:According to this wrong clock when the time is 59
minutes 55 seconds, it is 60 minutes in correct
clock.
The wrong clock, in 59 minutes 55 seconds loses 5
seconds. So in24 hours, it loses 120 seconds or 2
minutes.
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CLOCK
Question - 8
A clock is set right at 8 am. The clock gains
10 minutes in 24 hours. What will be the
true time when the clock indicates 1 pm on
the following day?
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CLOCK
Solution:Time from 8 am on a day to 1 pm on the following
day is 29 hrs.
Now, 24 hrs 10 min of this clock are the same as 24
hrs of the correct clock.
i.e.145/6 hrs of this clock = 24 hrs of correct clock.
29 hrs of this clock = (24*6/145)*29 hrs of correct
clock.
= 28 hrs 48 min of correct clock.
So, the correct time is 28 hrs 48 min after 8 am or
48 min past 12.
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Question - 9
CLOCK
A clock is set right at 4 a.m. The clock loses 20 min
in 24 hours. What will be the true time when the
clock indicates 3 a.m. on 4th day?
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CLOCK
Solution:Time from 4 am to 3 am on 3rd day = 24*3-1 = 71
hrs.
Now, 23(2/3)=71/3 hrs 40 min of this clock = 24 hrs
of correct clock.
or, hrs of this clock = 24 hrs of the correct clock.
Therefore, 71 hrs of this clock = 24*3*71/71=72 hrs
of correct clock.
So, the correct time = 3 am + (72-71) = 4 am.
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