Direct Proportion

Direct Proportion

Inverse Proportion

Before you study what is direct proportion, you are advised to read: What are Ratio's ? What is Proportion ? In Direct Proportion, two quantities change in such a manner that if one quantity increases, other quantity also increases in same proportion and vice-versa Or we can say that, when two quantities x & y increases or decreases together in such a way that the ratio of their corresponding values remains constant (i.e k), we can say x and y are in direct proportion. That is if: x/y = k or x = ky Then x and y are in direct proportion And when y1, y2 & y3 values of y corresponds to values x1, x2 & x3 of x., then we get: x/y = x1/y1 = x2/y2 = x3/y3 When two quantities, x & y are in direct proportion or vary directly, we write it as x ∝ y Example 1: Observe the following table: No. of Soft Drink bottles (1 ltr each) 1 2 4 7 9 Cost ( in $) 5 10 20 35 45 In the above you can see that cost of one soft drink bottle is 5$ and their ratio is 1/5 Now when number of bottle increases to 2; cost also increase to 10$, but here also there ratio is 1/5 You can observe the same pattern in subsequent columns that with increase in number of bottle, cost also increases in such a manner that their ratios remain constant i.e. 1/5 Therefore, we can say that number of soft drink bottles and cost are in Direct Proportion Example 2: Observe the following table: Diesel (in Litres) 2 4 5 8 10 Distance Travelled (in Km) 30 60 75 120 150 Above table represents consumption of diesel by car and distance travel by it: You can observe that to travel a distance of 30 km car consumes 2 litres of diesel. Suppose diesel consumed is x and distance travelled is y. Apply the above stated formula for direct proportion and we get: x/y = k 2/30 = k or k = 1/15 Hence, we get ratio 1/15 Now, you can check the subsequent values of x and y from the above table & you will observe that in all the cases; k = 1/15 Therefore, we can say that consumption of diesel by car and distance travel by it are in Direct Proportion