 ### Direct Proportion: Formula, Examples, Definition - Directly Proportional

In this blog, we will discuss direct proportions.

What is Direct Proportion?

Mani�s birthday is approaching. Also, she has won the badminton tournament, so she has to give treat to her friends. She wants to order a cold drink, pastry, and sandwich. The total cost of pastry, sandwich and cold drink is Rs30. Now she has to decide on how much budget is required and how many friends she can invite. So she decided to make a chart to sort it out. �

In chart, we can see that with the change in the number of friends the cost is changing.

Here is the number of friends is increasing the cost incurred is also increases. In this way, the increase or decrease can be expressed as a proportion. If the number of friends is denoted by x and cost by y then it can be expressed as x/y = k. x is directly proportional to y. Here x1/y1 = 1by 30, x2/y2 is also = to1/30 and so on. So we can say that x/y = 1/30 let us have some more examples of direct variation.

If a bus travels at a steady speed of 80 km per hour, the amount of fuel consumed is related to the distance traveled.

If a bus travel 10 km at a steady speed and consumed 0.5 liters of fuel and if the bus travel 20 km, the fuel consumption will be 1 litre and if the bus travels 30 km, the fuel consumption will be 1.5 liter.

The consumption would increase in proportion to the distances 40, 50 and 100 km.

See here the ratio of fuel and distance is same in each case. Notice that the ratios of the corresponding values of x and y is constant.

So we can say the consumption of fuel is directly proportional to the distance traveled.

The ratio of x to y is constant. So in this example, we can calculate the fuel consumption as k times the distance traveled, where k is equal to 1 upon 20.

When two quantities x and y are so related that their ratio remains constant, x upon y is equal to k or x is equal to ky, we say that x is directly proportional to y, or that x varies directly with y. The constant k is the constant of proportionality.

Example: An electric pole, 14 meters high, casts a shadow of 10 meters. Find the height of a tree that casts a shadow of 15 meters under similar conditions.

Solution: Let the height of the tree be x metres. We form a table. Note that the more the height of an object, the more would be the length of its shadow.Hence, this is a case of direct proportion. x1/y1 = x2/y2.14/10 = x/1514/10 x 15 = x.(14 x 3)/2 = x21=xSo x1 : x2 = y1: y214 : x = 10 : 15Therefore, 10 � x = 15 � 14x=(15 x 14)/10 = 21m