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so now we are going to see the theory
based on the clock problems clock
problems they ask very simple uh you
know they generally ask the angle formed
between the minute and hour end of a
clock in csi net examinations
and sometimes they also ask you question
regarding
a clock is fast
or a clock is getting slow than the
actual time based on that also they ask
question
so what you need to understand is very
simple uh things one is the relationship
between the minute and hour hand and uh
as a clock is a circle
so total angle is 360 degree for a clock
okay and how much angle is rotated by a
minute or hour and that's 360 degree
that's what you need to remember so
minutes peaks so basically if we think
about the small and large one so small
one
is a hour hand and large one a tall one
is a minute hand
so our hand rotates 360 degree and
rotation of 360 degree for an hour and
gives us 24 hours
and rotation of 360 degree for a minute
hand gives us
one hour
okay
and not 24 12 hours
and 360 degree rotation of a minute and
gives
one hour
okay or simply
so what we can write is that the angle
traced by the hour hand
hour hand 360 degree rest by minute hand
got it
so for an hour hand one hour equals to
how much 360 degree by 12
and for one minute by the minute hand
so minute hand
one minute duration
so for a minute and one minute duration
covers six degree of the clock for our
hand
one hour duration
covered by
got it
in
space over our hand that's quite true
because
the minute hand
rotates
independently but the hour hands
rotation depends on the minute hand
isn't it so
when we write
let's say this is 12
so if 3 pm is something like that
if it's 3 30
then the minute hand will be towards the
on the same position
it was before while it was 3 o'clock it
will be little bit shifted
between three and
four
between three and four because the hour
hands rotation depend on the rotation of
the minute hand
very very important
okay both ends of a clock coincide once
every hour remember that so in 12 hours
the coincidence will be 12 times
the hands of the clock are in the same
straight line
considering the opposite direction
and the superimposing also in the same
direction
when two hands of the clock at a right
angle 90 degree angle
the gap here
is between
when the two hands of a clock is at a
right angle or 90 degree angle there is
a 15 minute specs apart
when the hands of a clock are in the
opposite direction like this
then there are 30 minutes apart
forming right angle 15 minutes apart
both are in the opposite direction
minutes
apart
got it
and if the watch of a if a watch or
clock indicates 9 15 but the correct
time is 9 then it will be told as
too fast
and if the clock is showing for 8 45
when the correct time is 9
it will
told as 15 minutes too slow got it
what else
hands of the clock will be straight line
but opposite direction
this is the question that they ask in 24
hours how many times the hands of a
clock is present in the opposite
direction 22 times
just write it down just mug it up
the handles of a clock coincide 22 times
a day
the hands of a clock are straight
the hands of a clock are at right angles
remember that
these four are very very important you
can simply find it out why they are
saying this why we are talking like that
but
i am not explaining with the proof but
these are all the facts
the hands of a clock will be straight
line but opposite direction that means
this is the situation
that is 22 times
they'll coincide
like this same direction 22 times
straight
right angle
okay
two hands of a clock will be together
between h and h plus one o clock
can be divided like this ok we will find
it out quite easily
rest things are angles between the hands
of the clock very very important
angle between the hand of a clock what
we simply do you need to count uh the
angle
created by the minute hand
angle created by the hour hand
okay
and then we need to subtract them from
each other say x and y the simple value
will be x minus 1 x minus y will be the
angle the actual angle created between
the hour and minute hand that's how easy
it is
but remember one thing let's say they
say that
so 8 15 pm
at 8 15 pm what is the angle traced by
the minute and hour end of the clock if
that is the question how to solve that
so minute for minute it's 15 minutes
for hour
hour means eight hours
no remember i told you the hour hands
movement depends on minute hand so for 8
angle created will not be the same
so 8 hour
plus
into hour so 8 hour plus 15 divided by
converting minute into hour
that's how if we divide the minute into
a 60 we'll get a conversion of minute
into hour that will be our idea
so it'll be
got it
so now what we have 15 minutes and what
we discussed earlier
here
that a minute hand gives 60 degree hour
hand 30 degree 1 hour 30 degree 1 minute
so 1 minute 6 degree 15 minutes 15 into
right
same thing for hour and 1 hour 30 degree
so that is 33 by 4
hour into 30 degree
okay
so how what is this 2
and this will be 15
so what is the value
divided by
degree
so remember now what is the answer x
minus y that is
there is no point of you know minus
value here so simply 247
so at 8 15
the
angle between the minute and hour and
will be a 157.5 degree
got it and basically what will what we
can see in the 8 15 you can also see
that in the clock
be 8
something like 8
and
okay
this is the angle
this angle is created sorry this angle
is created and that's quite big bigger
than 120 degree this is 157.5 degree
okay
it
so now we will solve some clock problems
we've seen the formula it's quite easy
and again in clock problems also there
are shortcuts very simple shortcuts are
available i don't take them because the
more shortcuts you try to remember the
more information you need to process and
for this we know we are biology students
we are going to focus on things which
are
just required for the exams
qualification here and we are going to
use it for it so clock problems we are
going to use the traditional approach
of finding out the degree of angles
formed between the hour and minute hand
and let's solve some problem to find
this out okay so let's go
the first question okay
a clock is started at noon by 10 minutes
past five the hour hand has turned
through now again the the angle the hour
end is actually covered that's what they
want us here okay
so a clock has started at noon at noon
means 12 o'clock by 10 minutes past five
so at noon means starting from 12
o'clock and by 10 minutes past five that
means 5 and 10 5 10 p.m this is
basically the time and if the time in
the clock is 5 10 pm then the hour hand
how much degree the hour hand is
actually covered remember one thing the
total area the total uh area is 360
degree 360 degree area and which is
covered by trace by the hour and
by the hour and
and that is 12 hours okay
so for every single hour
it is 50 degree
okay now what is the total hour here 5
hours plus remember the hour hands
movement depends on the minutes movement
as well because if 10 minutes pass the
hour and also move based on the 10
minute so if you see a clock at 5 10 pm
and then if you see the clock at 5 30
you will see the small
the small arm of the clock is not in the
same position it will be little bit
moved right that is the idea so
our hands movement depends on minute
hand i already told it multiple times so
to convert that 10 minutes to hours and
how to convert minute to hours simply
divide it with
okay so it will give us
all right so for 1
from one hour it's 30 degree movement of
the hour end right and we know the total
hour here
hour is 30 degree so for 31 by 6 or it
is multiplied with 30
and this is
migrated to 155 degree that is the hour
and movement this is a very simple kind
of problem this kind of simple problems
will be asked in the clock and time
questions okay so let's move to the next
question
here okay let's take a different color
now an accurate clock shows eight
o'clock in the morning
through how many degrees will the hour
hand rotate when the clock
shows two o'clock in the afternoon see
so basically it's accurate clock or
wrong clock we don't need to understand
it's that means a normal clock a clock
showing eight o'clock in the morning
now from eight o'clock to two o'clock in
the afternoon what is the total degree
of rotation
done by the our hand done by the
our hand okay so again our hands
rotation what we know is that 12 hours
rotation 360 degree so 1 hours rotation
now the second concept that we need to
know here is that in this particular
case we need to know the time that is
from eight o'clock in the morning to two
o'clock in the afternoon and that is
six hours
total
six hours
basically
six hours so
for one hour the degree
covered the angle covered by the hour
and is 30 degree so for six hours
it will go for
degree so the option 8 is the correct
answer
see this is how easy it is you know this
is how easy it is to solve this kind of
clock problem so i always love the clock
problems to answer now let's take a
different color and third question the
angle between
the minute hand and the hour end of the
clock when the time is 8
matter in this kind of problem only the
degree of angle that matters the angle
between the minute and hour hand of the
clock so when the time is 8 30 what is
the angle between minute and hour and
many people may
try to draw a picture like this
say 8 30 means what this is our 3 this
is 9 so this is somewhere 8 is present
this is 6 so basically
this is the small hand and this is the
large hand so this is the kind of angle
that you can clearly expect and see and
you can clearly see this angle we are
seeing it's less than 90 degree this is
one from the logic purely based on the
logic and iq you can tell that yes the
angle must be less than 90 degree so of
course 90 degree you can see three
options are less than 90 degrees so csi
is also clever now let's try to solve it
with actual idea
now see the total is 8 hours and 30
minutes this is the time right we know
for the hour hand
we have the hour hand
and we have the
minute hand right
so for the hour hand
that means one hour 30 degree
for minute hands
one minute
now
eight so what we get for minutes one
minute 60 degree there are 30 minutes
so 30 into 60.
uh sorry it's three
three three degree for minute hand
it must be three degree not thirty
degree
because also for minute hand for sixty
minutes 360 degree
for one minute
six degree
right for one minute it's six degree
so for one minute it's six degree
so for 30 minutes here 8 min 8 hour 30
minutes so 30 minutes 13 to 60
now for the hour hand what is the value
traced by the angle traced by the hour
hand the angle pressed by the hour hand
must be 8 hours 30 minutes total
so we need to take account of the 30
minutes as well because remember one
thing
when the time says 8
only and 8 30 the hour ends movement is
also depending on the minute hand
because if it's 8 then the small hand
the hour end will be pointing shortly
towards eight but once it's 8 30
then the hour hand now move to between
eight and nine
right so
eight plus you will need to convert the
hour divided by 60
so that will give us what
so for 1 hour 30 degree
so 17
into 15
degree
so our hand pressed 255 degree minute
interest 180 degree then what we need to
do the difference
will give us the
difference
and that gives us
just what we thought
by looking at the the picture of the
clock that it must be less than 90
degree of course it's 75 degree the
angle created between the hour and
minute hand when the time is 8 30
whether it's morning or night the angle
is always 75 degree
got it
now let's move to another problem
a watch
which gains
uniformly in two minutes
gains uniformly in two minutes low at
noon on monday and in four minutes 48
second fast at 2 pm on the following
monday
when was it correct
now this kind of question is little bit
complicated the watch which gains
uniformly
gains uniformly is two minutes low
at noon on monday
and is four minutes 48 second fast at 2
pm
on the following monday
at noon means
so the time of that clock
two minutes low at 12 pm in the first
monday when we checked it
and then in the second monday when we
check it at 2 pm
we saw 4 minutes 48 seconds fast
throughout this time span
when was the clock correct
when was the clock showing the correct
time
so what we need to figure out here
the total time span
so we have monday
pm of that monday
to
we have 2 pm of next monday
right isn't it so what is the total time
span here so monday to monday 7 days
and 2 hours so what is the seven day
means 7 into 24
plus 2
and that gives us 170 hours
total 170 hours
in this 170 hours
what is the total gain
gains 2 minutes at the beginning and
here it also gaining 4 minutes 48
seconds
so first it gains 2 minutes
then it gains
so you need to count that minute right
so 4 minute
here
that will be the total minute because we
need to convert the
even because again the minute hand's
movement will depend on the seconds hand
isn't it the same concept
the our hands movement depends on the
mini science movement
the minute sense movement depends on the
second hand's movement
so this is the total time
[Music]
this much minute
okay
this much minute let's let's just find
out the value for it
this much minute
is gained
the clock gained this much minute 34 by
in 170 hours
okay
so
we know that earlier it was two minutes
gained later it was four point four
eight
four minutes 48 seconds gained
so we need to what we need to do we need
to
find out when it is working perfectly
simply if we go back
from this monday
so what we need to figure out is 34 by 5
minutes gained
so 34 by 5 minutes gained
in 170 hours
okay and we are finding out two minute
gain
two minute gain for how many much hours
two minute gain
that value
okay so one minute gained by this value
okay that gives us 50 hours
so try to understand now two minute gain
in 50 hours
so basically this same
this particular clock only low was two
minute low at the noon
and after that it continued to gain
and the gain goes
till four minutes 48 seconds fast till 2
pm on the next monday
and we found out what time taken
to gain 2 minutes so if you
rewind it back
if we rewind it back
then what we'll find
that two minute gain
will cancel the two minute loss
and that
clock will be in the right time showing
the right time
and that time came 50 hours
so what we can say
days
plus two hours
so two days two hours after the 12 pm on
monday
so try to understand this was early
monday
this was monday
this is another monday till this four
minutes 48 seconds fast
this is two minutes slow and this is
fast we found the way
a point a time point that is 50 hours
later that this first monday that is two
days two hours later from the first
monday when the clock is basically
showing the correct time
and that is
from monday two days two hours
and we are looking at 12 pm monday here
so two days means wednesday
and after two hours from 12 p.m means 2
pm
so wednesday 12 2 p.m
wednesday 2 pm is the time
when the clock showed the correct time
this question is not complicated all you
need to think what they actually asked
you to see the timeline the earlier
monday when you started with the end
monday where we were ending it
and the time frame in between
once you know that
the calculation is quite straightforward
the calculations are quite easy there is
no much no big deal on the calculation
but
you simply know that this 50 hours means
days and two hours is the time when the
clock because the clock range was two
minutes low then it became normal then
it became
four minutes 48 seconds fast so there
must be a place a time when the clock
was correct showing the correct time and
that's how we figured it out okay
you