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.)