Students can go through AP Board 8th Class Maths Notes Chapter 10 Direct and Inverse Proportions to understand and remember the concepts easily.

## AP State Board Syllabus 8th Class Maths Notes Chapter 10 Direct and Inverse Proportions

→ If x and y are in direct proportion, the two quantities vary in the same ratio.

i.e. if \(\frac{x}{y}\) = k or x = ky. We can write \(\frac{x_{1}}{y_{1}}\) = \(\frac{x_{2}}{y_{2}}\) [y_{1}, y_{2} are values of y corresponding to the values x_{1}, x_{2} of x respectively]

→ Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant. If y_{1}, y_{2} are the values of y corresponding to the values x_{1} and x_{2} of x respectively, then x_{1}y_{1} = x_{2}y_{2} (= k), or = \(\frac{x_{1}}{x_{2}}\) = \(\frac{y_{2}}{y_{1}}\)

→ If one quantity increases (decreases) as the other quantity decreases (increases) in same proportion, then we say it varies in the inverse ratio of the other quantity. The ratio of the first quantity (x_{1} : x_{2}) is equal to the inverse ratio of the second quantity (y_{1} : y_{2}). As both the ratios are the same, we can express this inverse variation as proportion and it is called inverse proportion.

→ Sometimes change in one quantity depends upon the change in two or more other quantities in same proportion. Then we equate the ratio of the first quantity to the compound ratio of the other two quantities.