2. There are tow types of variation :-
Direct variation.
Inverse variation.
3. DIRECT AND INVERS
PROPORTION
Direct proportion (variation): - Tow quantities x and y
are said to be in direct proportion ( variation ) if x
increases or decreases ,y also increases or decreases and
ratio of x and y remain constants that is x/y =k , where k
is positive numbers .
FOE EXAMPLE :- the cost of 2 kg of sugar is Rs 80
the cost of 4kg of sugar will be Rs 160
Here as the quantity of sugar increases the cost also
increases and ratio of quantity of sugar and it’s cost is
1:40
4. INVEARS PROPORTION ( VARIATION ) :- Tow
quantities may change in such a manner that if one
quantity increases , the other quantity decreases and vice
versa
FOR EAXAMPLE :- As the number of workers
increases , time taken to finish the job decreases .
Similarly , if we increase the speed , the time taken to
cover a given distance decreases .
5. Q.1 A machine in a soft drink factory fills 840 bottles sit
house . How many bottles will it fill in five hours ?
Ans :-
Number of bottles filled 6 hours 840 bottles
Number of bottles filled 5 hours ??? bottles
the given variation is direct.
Number of hours 6 hours 5 hours
Number of bottles 840 bottles ??? bottles
6/840=5/x
x = 5*840/6
x = 5* 140
x = 700 bottles
Hence , 700 bottles can be filled in 5 hours.
6. Q.2 A farmer has enough food to feed 20 animals
in his cattle for 6 days . How long would the food
last if there where 10 more animal in his cattle ?
Ans :-
Number of animals 20 animals 30 animals
Number of days 6 days Y = ???
the given variation is inverse
20*6 = 30*y
y = 20*6/30
y = 12/3
y = 4 days .
7. Q.3 A car takes to hours to reach a destination by
Travelling at the speed of 60 kg/h . How long will it
take when the car travels at speed of 80 kg/h ?
Ans :-
Speed in km/h 60 km/h 80 km/h
Time in hour 2 hours ??? Km/h
the variation is inverse .
60*2 = 80*y
y = 360*2/480
y = 3/2
Hence , it will take 1 and half hours to reach
the destination with 80 km/h speed .
8. GRAPH OF DIRECT PROPORTION
As we know that in Direct
Proportion if one variable
increases the other variable
will also increase, and both
of them increase at the
constant rate which keeps
the line of the graph
straight.
9. GRAPH OF INVERSE PROPORTION
In inverse proportion One
variable increases Where-as
the other one Decreases or
vice versa. So this does not
allow the graph to go on in a
straight line from the bottom
to the top, the graph of
inverse proportion will always
show the line from top to
Bottom.
