Direct and Inverse Proportions | Study

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 y₁, y₂ are the values of y corresponding to the values x₁, 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 y₁, y₂ are the values of y

corresponding to the values x₁, x₂ of x respectively then

^x1^{, Y}1 = ^x2^{, 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.

1. Distance and Time

2. Cost of Groceries

3. Cooking Ingredients

4. Speed and Fuel Consumption

5. Salary and Hours Worked