Need for Concepts of Variation
To find out the quantity of each item needed by Mohan or, the time taken by five students to complete the job, we need study some concepts of variation.
We will study the following types of variation:
- Direct variation
- Inverse variation
Direct proportion
Two quantities x and y are said to be in direct proportion if whenever the value of x increases (or decreases), then the value of y increases (or decreases) in such a way that the ratio x/y remains constant.
When x and y are in direct proportions, we have:
x1/y1=x2/y2=x3/y3
Inverse proportion
Two quantities x and y are said to be in inverse proportion, if whenever the value of x increases (or decreases), then the value of y decreases (or increases) in such a way that xy remains constant.
When x and y are in inverse proportion, then
x1 × y1 = x2 × y2 = x3 × y3, and so on.
Two quantities may be linked in two ways:
- Both increase or decrease together proportionally.
- If one increases, the other decreases proportionally and vice-versa.
The first way is named as direct variation whereas the second way is named as an inverse variation.
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