## Pre-Requisires

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**Direct and Inverse Proportions** | **Speed Notes**

**Direct and Inverse Proportions**

**Notes For Quick Recap**

**Variations: **If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. **(Scroll down to continue …)**

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**Direct Variation or Direct Proportion:**

Extra:

Two quantities x and y are said to be in **direct proportion **if they increase (decrease) together in such a manner that the ratio of their corresponding values remains

constant. That is if

=k [k is a positive number, then x and y are said to vary directly.

In such a case if y_{1}, y_{2 }are the values of y corresponding to the values x_{1}, x of x

respectively then = .

If the number of articles purchased increases, the total cost also increases. More than money deposited in a bank, more is the interest earned.

Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.

When two quantities x and y are in direct proportion (or vary directly), they are

written as

. Symbol

stands for ‘is proportion to’.

**Inverse Proportion: **Two quantities x and y are said to be in **inverse proportion **if an increase in x causes a proportional decrease in y **(and vice-versa**) in such a manner that the product of their corresponding values remains constant. That is, if xy

= k, then x and y are said to vary inversely. In this case if y_{1}, y_{2 }are the values of y

corresponding to the values x_{1}, x_{2 }of x respectively then

^{x}1^{, Y}1 = ^{x}2^{, y}2 or

=

When two quantities x and y are in inverse proportion (or vary inversely), they are

written as x

. Example: If the number of workers increases, time taken to finish

the job decreases. Or If the speed will increase the time required to cover a given distance decreases.

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