Direct and Inverse Proportions Class 8 Maths Notes - Chapter 13

When two variables change in the same sense i.e as one amount increases, the other amount also increases at the same rate it is called direct proportionality. When two variables such as x and y are given, y is directly proportional to x if there is non zero constant k. The constant ratio is called constant of proportionality or proportionality constant.

For example, If the cost of 1 kg of sugar is Rs.36, then what will be the cost of 8 kg sugar? It is Rs. 288. Similarly, we can find the cost of 3 kg or 5 kg of sugar. You can study the table below-

Direct and Inverse Proportions Class 8 Maths Notes

Two variables are said to be inversely proportional if the if one of the variables is directly proportional to the multiplicative inverse i.e reciprocal of the other. Two quantities change in such a manner that if one quantity increases, then the other quantity decreases and vice versa. The variable y is said to be inversely proportional to the variable x if there exists a non zero constant k. To understand this, let us look at the following speed and time situation.

For example, Zara can go to her school by walk, run, cycle or car. You can study the table below-

Direct and Inverse Proportions Class 8 Maths Notes

From the above table, it is clear that as the speed increases, the time taken to cover the same distance decreases.

Direct And Inverse Proportion Questions

  1. The mast of a model ship is 9 cm high, and the mast of the actual ship is 12 m high. If the length of the ship is 28 m, what is the length of the model ship?
  2. A loaded truck travels 14 km in a time duration of 25 minutes. How far can it travel in 5 hours if its speed remains the same?
  3. The number of students in a hostel is 100. Food provision is only for 20 days. If 25 more students join the group, how long will the provisions last?
  4. Below is a table of the car parking charges near a railway station –
Hours Rupee
4 60
8 100
12 140
24 180

Are the parking charges in direct proportion to the parking time?

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Practise This Question

39 men can build a bridge in 12 days, working 5 hours a day. In how many days will 30 men, working 6 hours a day, complete the work?