Inverse Proportion (Part - 5) - Direct and Inverse Proportion, Mathematics, CBSE Class 8 Video Lecture

hello friends this video and direct and
inverse proportion part 5 is brought to
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exam hello friends this video on direct
and inverse proportion part 11 is
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fear from exam so this was all about
direct proportion let us now talk about
inverse proportion now that we have
learned about direct proportion we will
know more about inverse proportion to
the name is sense paper that isn't
something which is exactly inverse of
what we have done in direct proportion
so here you see a birthday cake for a
birthday party okay
now let's say that 8 of your friends
reach at your birthday party and now you
need to give them tea so what do you do
you divide the screen into 8 equal
slices and give each slice of cake to
each of them yes now let's say that you
expected you invited a lot of friends
but instead of 8 from sixteen friends
arrived at the party so what will you do
because you can have just one birthday
cake
so what do you know this time you divide
the cake into 16 equal slices so that
you can eat one slice to eat now in that
case we notice something we see that in
case 2 the number of people increased
number of children increased as a result
what happened the size of each slice
between right now each slices smaller
whereas in the previous case each slice
would bigger so they shows that the size
of the slice is inversely proportional
to the number of pins so as the number
of kids increases the size of the slice
decreases so this is an inverse
relationship let's take one more example
so let me get if you have to decorate a
room for your friends
now there are key scenarios in the
person a zero you do it alone so you do
all the decoration alone and it takes
you two hours in the second scenario you
take help of the amount of friends and
two of you do it together and it takes
you one hour in the third scenario you
call a few other friends and the four of
you together do it and that time you
take fifteen to twenty minutes or the
same decoration so what does this show
to show that when the number of people
involved or the number of people who are
working for the Declaration that
increases with the time taken to
decorate decreases so here also the time
patience is inversely proportional to
the number of people involved in
decoration so these are some examples of
inverse proportion now let us talk about
speed in time so we have spoken about
distance time and speed before order to
this size we assume that the distance is
fixed let's see that we know that the
car has to travel from point A to point
B so this is the fixed distance so if
the distance is fit how speed and sign
good then let's say in the first
scenario the car travels with a very
high speed so in this case the time
taken by the car to travel from A to D
is maybe very small maybe some five
minutes so this is our phase one
so in case one we see that the speed of
the car let us assume that the speed of
the car is twenty four kilometers per
hour and the time T L by the car to
travel this distance ay B is five minute
the five minutes is five by sixty hours
that is one by twelve power
perfect okay now let's consider case two
where the car is traveling with a
measured speed so this time in case to
the value of speed is two kilometers per
hour
now since the speed is natural car is
moving slowing therefore the time taken
is more so this time the time taken to
cover the same distance ay B is one hour
so what's happening here is in this case
we see that it distances same speed
increases time decreases if speed
decreases time increases so there is an
inverse proportion relationship between
speed and time provided distance is
fixed so looking at this what can you
see we can see that in this case if you
look at case 1 we see speed into time is
equal to 24 into 1 by 12 which is equal
to 2 kilometers in the second case on to
speed into time is equal to 2 into 1
which is equal to 2 kilometer so
basically we see that the value of speed
into timing is same in both the cases so
this is another example which shows that
speed and time are inversely
proportional to each other as speed
higher the speed letter that I'm letter
to speed I know design provides a
distance to space so water inverse
proportion so when two quantities x and
y are said to be in inverse proportion
if X into my it is equal to K so in this
case the ratio doesn't remain constant
as instead the product of the people
quantities remain constant let us take
the same example as we took a the
previous
so we saw that in case one the speed of
the car was 24 km/h and in this case
time taken was 1 by 12 hour and in case
number 2 heed of the car world 2 km/h
and time taken was one hour so these
whether to inadvertently consider so
what are the two quantities involved
speed and size so let us see if speed is
the variable age and time is let 50 so
just assume that these are two different
quantities X and T so in this case what
do we see
metal engine this value at X 1 this
value as T 1 this value at X 2 and this
corresponding manual TT to be very
creative option observe that X 1 T 1 is
equal to 24 into 1 by 12 equals 2
kilometer and if 2 T 2 is equal to 2
into 1 which is equal to 2 kilometers
again so from this we see that X 1 T 1
is equal to X 2 T 2 that means at all
instants of time is the product of these
two quantities will always be constant
therefore if x and y added inverse
proportion we can write that X 1 y 1 is
equal to X 2 y 2 is equal to K so this
is the concept of inverse proportion now
later thank you
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