Students can go through AP 8th Class Maths Notes Chapter 13 Direct and Indirect Proportions to understand and remember the concepts easily.
Class 8 Maths Chapter 13 Notes Direct and Indirect Proportions
→ 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, x2 of x respectively then \(\frac{\mathrm{x}_1}{\mathrm{y}_1}\) = \(\frac{\mathrm{x}_1}{\mathrm{y}_1}\).
→ 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. Tfiat 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 \(\frac{\mathrm{x}_1}{\mathrm{x}_2}\) = \(\frac{\mathrm{y}_2}{\mathrm{y}_1}\)
Concepts of Variation :
→ Constants: 5, 10, 0, – 8. – 7,…. all these are constants values of these are always fixed irrespect of time, place.
→ Variables : temperature, wind speed, rainfall, price of a share, price of oil, etc. values of these depend on some other parameters hence they change from time to time, (or) place to place. So we call them variables.
The way they change is called variation In the middle classes we learn two types of variations. They are :
- Direct variation (or) Direct Proportion
- Indirect (or) inverse variation (or) Indirect proportion.
In higher classes we learn some other variations like combined variation, partial variation, etc ….
→ Direct variation : Perimeter of a circle depends on its radius in a fixed way. So, Perimeter (c) is directly proportional to its radius (r)
Price of petrol pumped into our tank is directly proportional to price of 1 litre petrol.
→ Price of painting is directly proportional to the area painted …. etc are some examples.
→ Direct Proportion: If the change in one variable is in same rate of change in other variable then they (two variables) are in direct proportion.
If x, y are two variables in direct proportion then we write it as x ∝ y (read as ‘x’ is directly proportional to ‘y’)
∝ – (proportional) is the symbol we use.
When x ∝ y ; then their ratio is always fixed and it is called proportional constant.
If x ∝ y ⇒ \(\frac{x}{y}\) = ky (proportional constant) or (rate of change) or x = ky
IMP : If the ratio is not same everytime then we cannot say they are in direct proportion.