### Direct and Inverse Proportions - Revision Notes

CBSE Class 8 Mathematics

Revision Notes

Chapter – 13

Direct and Inverse Proportions

Revision Notes

Chapter – 13

Direct and Inverse Proportions

- 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.
- Direct Variation or Direct Proportion:

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, Y1 = x2, y2 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 will decrease.