L1: Introduction - Direct and Inverse Proportion, Mathematics. CBSE Class 8 Video Lecture

hello friends this video on direct and
inverse proportion pac-man is brought to
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exam topics to be covered in this lesson
our introduction direct proportion
inverse proportion as problem solving
using direct and inverse proportion so
what are we going to talk about in
direct and inverse proportion let's look
at this example to get a brief idea
about what was all about this lesson
okay let's say that you have this car
and this car travels certain amount of
distance in certain period of time so
let us assume that the speed of the car
is uniform that is the car all these
travels with the same speed okay now
let's say that the car traveled maybe 1
kilometer in 5 minutes right so let's
make a lot of these numbers so in five
minutes the car covered one kilometer
now let's say that in another five
minutes that is a total of 10 minutes
now say 10 minutes how much distance
with the car covered it covers 2
kilometers similarly 4050 minutes how
much distance the car covered it would
have covered three kilometers and so on
so basically what we are seeing is is
that as the time increases the car
covers more distance now since the car
is always traveling with the same speed
so there is no doubt that sometimes the
car might travel fast sometimes it might
travel so that possibility is ruled out
so the car is always traveling with the
same speed now move the time if you ask
the car to travel for one hour it will
cover both kilometers if you ask the car
to travel only for five minutes it will
cover next kilometers right so as the
time increases the distance also
increases so what do we understand from
this
considering speed is same we find that
as time increases as P increases what
happens the distance covered also
increases the T increases D increases in
such a way that the ratio of time to
distance always remain constant so that
means if you look at these values these
are just some simpler values you would
see that the Dacians all always the same
in all the three cases whether you find
out the ratio of distance by time or the
ratio of time by distance everywhere
this ratio is the same let the ratio of
time to the stencil 5 into 1 in all the
three cases so in this case we see that
time and distance they are directly
proportional to each other that means as
time increases distance also increases
similarly as distance increases time
also increases so this possibility holds
true only when the assume that the baton
is traveling with the uniform speed let
us look at another example let's say
that you went to a clothes shop and you
want to buy some clothes maybe you want
to get a dress stitched and for that you
need clothes so now what happens let's
say that you have many varieties of
clothes in that store and you choose
this particular variety of cloth so now
you will be tending to shopkeepers how
much cloth do you need how much what is
the length of the cloth that you need
now how has the cost of the cloth
dependent on the length of the clock now
let's say that you see that you need two
meters of cloth so the cost of two
meters is rupees hundred that's what the
shopkeeper has told you not readily you
thought that no I think two meter will
not be sufficient so I would need mode
right so maybe you say that instead of
two
I'll need some six meters of clothes or
some four meters of clothes so what's
going to be the cost of 6 meters of
cloth the thick needles mean you
multiplied the initial two meters by
three so basically you multiply it by
three
so therefore the cost also increases
right now the shopkeeper going to give
you 6 meters of cloth for 600 because he
gives two meters 400 so hundred also
will get multiplied by P so when you ask
him for 6 meters we would charge you to
keep 300 similarly if you are think of
give you 10 meters of cloth what would
be the cost the cost will also get
multiplied because 10 meters meet you
will multiply the first one by 5 so 2
into 5 is 10 so there is a cost of 2
meters 100 so this would also get
multiplied by 5 so for 10 meters he
would charge you to be 500 so what are
the same and the length of the plot
increases the cost or 3 so that means
length and cost these are the two
quantities which are directly
proportional to each other so in this
case also the ratio of the cost to the
length remains constant at all times for
example in the first piece if you look
at the ratio of cost by net then it is
100 by 2 which is equal to 50 is to 1 in
the second case what is the ratio it is
300 by 6 which is again equal to 50 is
to 1 in the third case it is 500 by 10
which is again equal to 15 to 1 so the
ratio of the cost to the length of the
cloth remains constant as all
independent so here this is another
example where we see that two quantities
length and cost are directly
proportional to each other
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