NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

Class 8 is a good time for students to build a strong foundation in an important subject like mathematics which will help them secure good career options in later stages of their academic life. That is why the highly experienced team of CoolGyan has designed the NCERT Solutions for Class 8 Maths Chapter 13 meticulously to suit the needs of class 8 students. By availing of our Class 8 Maths Direct and Inverse Proportion Solutions, you can get the most accurate answers to every question in this chapter. The NCERT Solutions for Class 8 Maths Direct and Inverse Proportion have been prepared based on the current guidelines; hence they are the most online reliable source for securing high scores in your maths exams. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 8 Science, Maths solutions and solutions of other subjects also.

NCERT Solutions for Class 8 Maths Chapter 13 Free PDF Download

The expert team of CoolGyan has made available the Class 8 Maths Direct and Inverse Proportion solutions in PDF format on its official website. You can easily download the NCERT Solutions of Class 8 Maths Chapter 13 PDF from anywhere anytime and save it on your devices for offline access. The solutions are also printable so that you could even have a group study with the hard copy of the PDF.


We Cover all Exercises in the Chapter Given Below:

Exercise 13.1 - 10 Questions with Solutions.

Exercise 13.2 - 11 Questions with Solutions.


Chapter 13 - Direct and Inverse Proportions

13.1 Introduction

In the first section of Class 8 Maths Chapter Direct and Inverse Proportion, there are many examples given from daily life where the knowledge of proportions is applied. For example:

  • If two students arrange chairs for an assembly in 20 minutes, how much time will 5 students take?

  • If you have to make tea for 1 person and you use 1 teaspoon of sugar then how many teaspoons would you need for making tea for 5 people?

From these examples, it can be figured that there is a direct relation in a change of one quantity on another quantity. This can be understood better with the concept of variation. The variation between two objects means that quantities of two objects are related to each other in a way that an increase or decrease in one quantity leads to an increase or decrease in the other quantity.


13.2 Direct Proportion

You will learn the definition of direct proportion in this part of Direct and Inverse Proportion class 8 solutions. Two quantities x, and y, are said to be in direct proportion if they fulfill the following criteria:

  • If x increases, y increases too.

  • If x decreases, y decreases too.

  • x/y = C where C is a constant or, x = C * y. This means that the ratio of the respective values of x and y remain the same despite an increment or decrement in their values.

  • From the above rule, we can say that if for the value of x at x1 the value of y is y1 and for the value of x at x2 the value of y is y2 then x1/y1 = x2/y2.

We denote y is proportional to x by the symbol ∝ , i.e. y ∝ x. A real-life example of direct proportion is that if the number of things you purchase increases, there is an increase in expenditure too.


13.2 Inverse Proportion

This part of Direct and Indirect Proportion class 8 will acquaint you with the concept of Inverse Proportion. Two quantities x, and y, are said to be in inverse proportion if they fulfill the following criteria:

  • If x increases, there is a decrease in y.

  • If x decreases, there is an increase in y.

  • x * y = a constant K. This means that the ratio of the respective values of x and y remain the same despite an increment or decrement in their values.

  • From the above rule, we can say that if for the value of x at x1 the value of y is y1 and for the value of x at x2 the value of y is y2 then x1 * y1 = x2 * y2= C.

We denote y is inversely proportional to x by the notation y ∝ 1/x. A real-life example of inverse proportion is that if the speed of a car increases, the time to reach a destination will decrease.


Key Features of NCERT Solutions for Class 8 Maths Chapter 13

The solutions provided for Maths chapter Direct and Inverse Proportion of Class 8 by the subject matter experts at CoolGyan is apt for the students of class 8 because:

  • You can download the PDF of the entire solution and do a quick revision anytime at your pace, without the indeed of internet connection.

  • The solutions are most accurate and formulated after extensive research.

  • The team of CoolGyan is always available to help you out if you find any of the problems difficult to understand.

  • It is totally free of cost and a reliable online resource.

FAQs (Frequently Asked Questions)

1. What are the Various Methods to Solve Direct Proportion Problems? Explain any one of them with an Example.

There are two methods that can be used to solve direct proportion problems and they are:

  • Tabular Method

  • Unitary Method - We will understand this method with an example.

Problem - Let us say a worker gets 1000 Rs for working 2 hours. If he gets a salary of 3000 then how much time has he worked in total?


Solution - We know that for two quantities x and y in direct proportion we have x/y = C (constant). Applying this concept here we get:


C = number of hours worked/payment received by the worker for that duration = 2/1000 = 1/500.


So, if x = C * B we get x = 1/500 * 3000 = 12.

So the worker worked for 12 hours to receive a total payment of 3000 Rs.

2. Explain the Concept of Inverse Proportion Between two Quantities with an Example.

Here is a sample problem on the inverse proportion concept:


Problem - If it takes 4 days for 20 laborers to lay the foundation of a building, then how much time will 16 laborers take to do the same job?


Solution - If 20 laborers lay the foundation in 4 days then the duration in which 1 laborer can finish the job = 20 * 4.

To get the duration taken by 16 laborers we have = (20 * 4)/16 = 5 days.

3. What are the key features of using the NCERT Solutions of Chapter 13 of Class 8 Maths?

The key features of using the NCERT Solutions of Chapter 13 Direct and Inverse Proportion of Class 8 Maths are highlighted below:

  • These NCERT Solutions help Class 8 students to understand Chapter 13 Direct and Inverse Proportions clearly. They make all the important concepts of the chapter crystal clear to the students. 

  • The NCERT Solutions enables students to revise significant concepts of the chapter quickly. 

  • They are the best study material to prepare for the Class 8 Maths exam as they are formed after extensive research done by the best Math professionals that tend to provide accurate information. 

4. What do I have to do to download the NCERT Solutions of Chapter 13 of Class 8 Maths?

In order to download the NCERT Solutions of Chapter 13 Direct and Indirect Proportion, you have to go through the given steps:

  • Visit the page NCERT Solutions of Chapter 13 Direct and Indirect Proportion of Class 8 Maths.

  • On that webpage, you will find different study materials other than the NCERT Solutions. It will include revision notes, textbook questions answers, sample papers, mock test papers, etc. 

  • After selecting your desired study material click on the download icon. 

5. What are the topics covered in Chapter 13 of Class 8 Maths?

Chapter 13 Direct and Inverse Proportion covers three topics in total. These are the introduction of the chapter, Direct Proportion, and Inverse Proportion. You can understand these topics thoroughly on CoolGyan. This platform helps students to comprehend Maths subjects easily. It also provides various facilities like video lectures, sample papers, and test papers to prepare well for their exams. 

6. What is the actual length of the bacteria if it has enlarged 20,000 times? The initial length of the bacteria is 5cm when it is enlarged 50,000 times. 

Let us consider the actual length of the bacteria to be x cm. If the bacteria attains a length of 5cm after enlarging 50,000 times, then applying the unitary method, the length of the bacteria will be x cm if it enlarges 20,000 times. 

Enlargement                                                                              Length

50,000                                                                                         5 cm

20,000                                                                                         x cm 

After cross multiplying, the original length of the bacteria is 

Original length= 5/50,000 cm = 1/10,000 cm 

Since both the quantities are directly proportional to each other. 

50,000/20,000= 5/x

50,000*x= 5*20,000

x=5*20,000/50,000

x= 2cm

7. What should I do to get good marks in Chapter 13 of Class 8 Maths?

To get good marks in Chapter 13 Direct and Inverse Proportion of Class 8 Maths, you have to attend all the lectures related to the chapter at school. You must pay attention to what your teacher is teaching. Then, invest time in doing a proper revision when you reach home. Make notes of the chapter containing essential concepts and formulas so that you can revise the entire chapter in a short period. Moreover, you are recommended to thoroughly go through the NCERT Solutions of Chapter 13 of Class 8 Maths available free of cost on the CoolGyan website and the CoolGyan app.