NCERT Solutions for Class 8 Maths Chapter 11 Direct and Inverse Proportions - PDF Download

NCERT solutions for class 8 maths chapter 11 Direct and inverse proportion cover the most fundamental concepts of proportion. Chapter 11 effectively enriches the understanding of Direct and inverse proportion by providing practical examples and exercise questions. Direct and inverse proportions are used to find the relationship between the quantity and the amount. The quantities are also referred to as directly proportional and inversely proportional. Direct proportion is an increase or decrease of two quantities at the same time. Inverse proportion is a decrease of one quantity for increasing values of another quantity. The symbol used to indicate proportionality is "∝".

NCERT solutions for class 8 maths chapter 11 Direct and inverse proportion is designed by eSaral’s expert teachers of maths to help students practice more questions and overcome their doubts about the concepts and topics covered in this chapter. A set of exercise questions has been formulated in PDF format and answered in a straightforward and logical manner, utilizing sequential problem-solving strategies.

NCERT solutions for class 8 maths chapter 11 are designed by experts to help students think logically and analytically. To practice more questions, please click the link below to download the free PDF of NCERT solutions of chapter 11 developed by subject specialists from eSaral. 

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Important Topics covered in Chapter 11 - Direct and Inverse Proportions

Chapter 11 of class 8 maths is related to Direct and Indirect proportion. This chapter is considered as one of the most important chapters in maths. The following topics are mentioned in this chapter:

11.1 Introduction - In the first part of the class 8 maths chapter Direct and Inverse proportion, many examples are shown from everyday life where the concept of proportion is used. For example:

• if you need to make tea for one person and use one teaspoon of sugar, how many teaspoons would it take to make tea for five people?
• If two students set up chairs for a gathering for 20 minutes, how long will it take 5 students to do the same?

It follows from these examples that the relationship between a change in one quantity and a change in another quantity is directly related. This relationship can be explained in more detail with variation. The difference between two objects implies that the quantity of two objects is related in such a way that the increase or decrease of one quantity increases or decreases the other quantity.

11.2 Direct Proportion -  In this section, you will learn how direct proportion is defined in Direct and inverse proportion class 8 solutions. A quantity x and a quantity y are said to have direct proportion if they satisfy the following conditions:

• 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. Direct proportion is a real-world phenomenon in which, as the quantity of items purchased increases, so does the expenditure.

11.3 Inverse Proportion - Inverse proportion: This part of the Direct and Indirect proportion class 8 will familiarize you with inverse proportion. Two quantities x and y are said to have inverse proportions if they satisfy the following conditions:

• 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 even if x and y increase or decrease, the ratio of x to y remains constant.
• 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. In real life example, the inverse proportion means that if you increase the speed of your car, the time it will take you to get to your destination will decrease.

NCERT Solutions for Class 8 Maths Chapter 11 Exercises

These NCERT solutions are structured in such a way that you will get a clear understanding of all the concepts with the help of simple exercise questions. Try the exercises below to learn and practice NCERT solutions for class 8 maths direct and inverse proportion.

Benefits of Downloading The NCERT Solutions for Class 8 Maths Chapter 11 - Direct and Inverse Proportions

Students can effectively prepare for their examinations by practicing the important questions of class 8 mathematics chapter 11 available on the eSaral website.

Here are some benefits of solving class 8 math chapter 11 important questions:

1. All the important questions in class 8 maths chapter 11 have been solved and complemented with the necessary formulas and explanations by our experienced faculty of maths so that the students can comprehend the concept well and gain overall clarity.
2. You can also download a free PDF of the complete solution and make a quick revision at your own speed.
3. These NCERT solutions provided by eSaral are the most precise and formulated after thorough analysis by our expert teachers.
4. The NCERT solutions PDFs are written in easy and comprehensive language to understand the topics and concepts easily.

Frequently Asked Questions

Question 1. What is Direct Proportion in NCERT solutions for class 8 maths chapter 11 ?

Answer 1. 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. 

For example: if 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 x1/y1=x2/y2.

Question 2. What is Inverse Proportion in NCERT solutions for class 8 maths chapter 11 ?

Answer 2. 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. 

For example: 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 x1/x2=y2/y1.