CLASS-7INVERSE VARIATION

Inverse Variations

If two quantity ‘A’ & ‘B’ are said to vary indirectly or be in inverse variation or in inverse proportion, if they change in such a way that the ratio of two values of ‘A’ is the same as the inverse ratio of the corresponding two values of ‘B’. In a simple way to better understand we can say that, number of workers inversely or proportionately varies, if the number of workers increases then given work can be finished a very short period of time but if the number of workers reduces then to complete the same job more days are needed.

Example.1) If a project can be finished by 20 people within 10 days, if 10 people left the job then the rest of the people take how many days to finish the same project ?

Ans.) As per the given condition, if 20 people finish the project by 10 days. Then, 1 people can finish the same project by (10 X 20) = 200 days [as per the inverse variation if the number of people reduce then to complete the same project it will take more days then earlier defined]

10 X 20

Now, (20-10) = 10 people can do the same project by -----------

10

= = 20 days              (Ans.)

Example.2) In a military base camp there are enough foods for 1500  soldiers for 24 days, if 500 soldiers shift to other camps then how long will the food last ?

Unitary Method

If there are the food of 1500 soldiers for 24 days

Then the same food goes of 1 soldier is  = 1500 X 24

Now the same food will go for 1500 – 500

1500 X 24

= 1000 soldiers is =  --------------  =   36 days     (Ans.)

1000

Here you can observe that, cost & product indirectly varies, if the food quantity increase then the number soldiers decrease.

Proportion Method

When there are 1500 soldiers, the food is enough for 24 days but when there are 1000 soldiers, let it last for x days. Here you can observe that, cost & product quantity indirectly varies, if the food quantity increase then the number of soldiers decrease, clearly, this is the case of inverse variation

So, then the ratio of the numbers of soldiers = the inverse ratio of the number of days of food remains –

That is 1500 : 100 = x : 24

1500                 x

------------  =  ----------

1000                24

1500 X 24  =  x X 1000

1500 X 24

x  =  --------------- =  36 days        (Ans.)

1000

Multiplying Ratio Method

Here the two quantities (time & number) are in the indirect proportion. The number increases in the ratio 1500 : 1000 =  x : 24

So, the value also increases in the same ratio, hence the multiplying ratio is  15 : 10 = 3 : 2

3

So, the required value would be =  -----------  X  24

2

=  3 X 12 =  36 days        (Ans.)