INVERSE VARIATION IN UNITARY METHOD
Inverse Variation :
Please look at the following situations.
More men -----> Less days to complete a work
More speed -----> Less time to cover the distance
More vehicles on the road -----> Less road space
Less time per day -----> More days to complete the work
Thus we can say, if an increase in one quantity produces a proportionate decrease in another quantity, then the quantities are said to be inverse variation.
or
If a decrease in one quantity produces a proportionate increase in another quantity, then the quantities are said to inverse variation.
Changes in the quantities must be opposite.
That is,
Increase -----> Decrease
or
Decrease -----> Increase
Unitary Method :
Unitary method is all about finding value to a single unit.
Unitary method can be used to calculate cost, measurements like liters and time.
In this section, you will learn how inverse variation problems can be solved using unitary method.
Example 1 :
10 workers can build a wall in 12 days. How many days will 15 workers take to build the same wall ?
Solution :
This is a situation of inverse variation.
Because,
Number of workers increases ----> Number of days will reduce
Given : 10 workers can build a wall in 12 days.
No. of days taken by one man to complete the work is
= No. of men ⋅ No. of days
= 10 ⋅ 12
= 120 days
No. of days taken by 15 men to complete the work is
= 120 / 15
= 8 days
Therefore 15 workers will take 8 days to build the same wall.
Example 2 :
In an army camp provisions were there for 500 men for 28 days. If 400 men attended the camp then how long did the provisions last ?
Solution :
This is a situation of inverse variation.
Because,
Number of men decreases ----> Number of days will increase
500 men ---> 28 days
1 men = 500 ⋅ 28
For 400 men = (500 ⋅ 28) / 400
= 35
Therefore provision is enough in 35 days for 400 persons
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