### Direct and Inverse Proportions - Revision Notes

CBSE Class 8 Mathematics
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 $\frac{x}{y}$=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 $\frac{{x}_{1}}{{y}_{1}}$ = $\frac{{x}_{2}}{{y}_{2}}$.
• 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 $x\propto y$. Symbol $\propto$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, xof x respectively then  x1, Y1 = x2, y2 or $\frac{{x}_{1}}{{y}_{1}}$ = $\frac{{x}_{2}}{{y}_{2}}$
• When two quantities x and y are in inverse proportion (or vary inversely), they are written as x $x\propto \frac{1}{y}$. 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.