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Direct and Inverse Proportions Class 8 Maths Chapter 11 CBSE Notes - 2025-26

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Maths Notes for Chapter 11 Direct and Inverse Proportions Class 8 - FREE PDF Download

In Cbse Class 8 Maths Notes Chapter 11, you’ll discover all about mensuration — how to measure the area, perimeter, and volume of different shapes. This chapter makes it easy to understand formulas for rectangles, squares, circles, and even 3D figures like cubes and cylinders. If you ever felt confused by so many formulas, these notes break them down step by step for you.


Learning this chapter becomes easier with our Class 8 Maths Revision Notes. They help you quickly revise all key concepts, so you feel confident before exams. Vedantu’s notes are made to be simple, clear, and perfect for last-minute revision.


Mensuration also comes up often in exams, so understanding it well can really help boost your overall score. It’s a chapter that teachers always highlight as important in Maths.


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Access Class 8 Maths Chapter 11 – Direct and Inverse Proportions

Variations And Proportions:

When the values of two quantities depend on one another in a way, such that the change in one quantity causes change in the other, the two quantities are said to be in variation.

Direct Proportion:

  • Two quantities a and b are said to be in direct proportion if they vary i.e., they increase or decrease together in such a manner that the ratio of their corresponding values remains constant. That is if ab=c [c is a positive number, then a and b are said to change directly.

  • To explain the condition, let a1,a2 be the two values of a and b1,b2 be the values of b, then a1b1=a2b2.

  • To represent two quantities related proportionately, we write ab.

Examples Of Direct Proportion: 

  • If the quantity of petrol in a car increases, the total distance covered also increases.

  • If the radius of a circle increases, the area of that circle also increases.

Inverse Proportions: 

  • The two quantities a and b are said to be in inverse proportion if an increment in one causes a proportional decrement in the other or if an decrement in one causes a proportional increment in the other that is, the product of their corresponding values remains constant. Which means, if ab=c or a=cb [c is a constant], then a and b are said to vary inversely. 

  • To explain this case, let a1,a2 be the two values of a and b1,b2 be the values of b, then a1b1=a2b2

  • To represent two quantities related inversely, we write a1b

For example:

As the speed of a vehicle(bike) increases, the time taken to cover a particular distance decreases.


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Download Maths Direct and Inverse Proportions Revision Notes PDF

Different study material, solutions to the problems, revision notes, sample papers, and previous year question papers provided by Vedantu are helpful to the students to a great extent.


  • Access Class 8 Maths Chapter 11 Direct and Inverse Proportions Revision Notes in PDF format on Vedantu's official website and mobile app.

  • Vedantu aims to ensure comprehensive learning for every student, providing solved answers to enhance understanding and improve scores.

  • Utilize Vedantu Revision Notes as a reliable last-minute resource for effective preparation and revision before final exams.


About Direct and Inverse Proportion

There are so many situations in our life where we see some direct or indirect relationship between two things, like

  • If the number of things purchased is increasing then the bill amount to pay also increases. (direct).

  • If the speed of the car will increase then the time to reach the destination will decrease. (indirect).

Any two physical quantities that vary is said to be proportional according to Mathematics if they are multiplicatively connected to each other by a constant term. For example, the more we eat, the more energy we gain, and the more we run, the more energy we lose.

There are two kinds of proportionalities in Mathematics.

When one quantity increases along with the other then it is called directly proportion whereas if one increases and the other decreases then it is inversely proportional.

  • Direct proportion meaning: Two quantities are said to be directly proportional to each other if the ratio of their values is constant at any instant of time. The increase in one quantity results in the increase of the other. For example, the more we exercise, the more fit is our body.

  • Inverse proportion: Two quantities are said to be inversely proportional to each other if the product of their values at any instant is a constant. The increase in one quantity results in a decrease in the other. Example: The more we eat junk, the less is our physical fitness.

The key difference between direct and inverse proportion are listed in the table below:

Difference Between Direct and Inverse Proportion

Direct Proportion

Inverse Proportion

The two measurable quantities vary directly with each other.

The two physical quantities vary inversely with each other.

The increase in one quantity results in the increase of the other. 

The increase in one quantity decreases the other.

The decrease in one quantity results in a decrease of the other.

The decrease in one quantity results in the increase of the other.

The ratio of the values of two quantities at any instant is constant.

The product of the values of the two quantities at any instant is a constant.

Ex: Force and work

If the amount of force applied increases, the amount of work done also increases, and vice versa.

Ex: Pressure and volume

The volume of any substance decreases with the increase in pressure and vice versa,

Symbol Of Proportion

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When two quantities say l and m are in proportion, then they are written as l ∝ m where ∝ represents “is proportion to”.

There are two methods to solve the problems related to direct proportion-

  1. Tabular Method

  2. Unitary Method

Why Choose Vedantu for Direct and Inverse Proportion Revision Notes?

  • Vedantu's mathematician experts have crafted these revision notes to encompass vital concepts, equations, formulas, and solved examples.

  • The revision notes aim to boost students' confidence, empowering them for better performance in their final exams.

  • Aligned with the updated CBSE syllabus, Vedantu's Revision Notes ensure relevance to current educational standards.

  • Highly qualified teachers at Vedantu strategically emphasize key topics, aligning with the exam perspective.

  • Students can rely on these notes for a comprehensive understanding and effective exam preparation.


Conclusion

For an enhanced comprehension of this subject, NCERT - Class 8 Maths Chapter 11 - Direct and Inverse Proportions, thoughtfully prepared by experienced educators at Vedantu, is your invaluable companion. These notes break down the complexities of Direct and Inverse Proportions into easily digestible sections, helping you grasp new concepts, master formulas, and navigate through questions effortlessly quickly in the last minute as well. By immersing yourself in these notes, you not only prepare for your studies more efficiently but also develop a profound understanding of the subject matter.

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FAQs on Direct and Inverse Proportions Class 8 Maths Chapter 11 CBSE Notes - 2025-26

1. What key concepts are summarised in the Class 8 Maths Revision Notes for Chapter 11, Direct and Inverse Proportions?

These revision notes provide a concise summary of the core concepts for Chapter 11. They cover the fundamental definitions of direct proportion and inverse proportion, how to identify the relationship between two quantities, and the use of the constant of proportionality (k). The notes also include key formulas and methods for solving word problems related to this chapter.

2. How can I quickly determine if a problem involves direct or inverse proportion during a revision?

A simple way to check is to see how the quantities relate. Ask yourself: if one quantity increases, does the other also increase? If yes, it is direct proportion (e.g., more articles purchased, higher the cost). If one quantity increases while the other decreases, it is inverse proportion (e.g., more workers on a job, less time taken to complete it).

3. What is the main formula to remember for a quick revision of direct proportion?

For a quick revision of direct proportion, the most important formula to remember is that the ratio of the two quantities (x and y) is always constant (k). This is expressed as:

  • x/y = k or, more practically for solving problems, x₁/y₁ = x₂/y₂.

4. What is the core principle for solving problems on inverse proportion mentioned in these notes?

The core principle for inverse proportion is that the product of the two quantities (x and y) remains constant (k). The formula to remember for revision is:

  • x * y = k or, for problem-solving, x₁ * y₁ = x₂ * y₂.

5. Why is the product of two quantities constant in inverse proportion, while their ratio is constant in direct proportion?

This is because of their fundamental relationship. In direct proportion, two quantities increase or decrease at the same rate, so their ratio (like speed, which is distance/time) remains the same. In inverse proportion, one quantity's increase causes a corresponding decrease in the other to keep a final outcome fixed (like total work done), so their product (e.g., speed × time = fixed distance) remains constant.

6. What is a common mistake to avoid when applying the concepts from these revision notes?

A very common mistake is confusing the formulas. Students often use the direct proportion formula (x₁/y₁ = x₂/y₂) for an inverse proportion problem. During revision, it's crucial to first identify the type of proportion correctly and then apply the appropriate formula: ratio for direct (x/y) and product for inverse (x*y).

7. How do these Class 8 Maths notes help in structuring a quick revision of Chapter 11?

These notes are structured to facilitate a quick and effective revision. They start with the basic definitions, move to the identifying characteristics of each proportion, provide the essential formulas, and conclude with solved examples. This logical flow allows students to recap the entire chapter systematically, reinforcing their understanding for the CBSE 2025-26 exams without needing to read the whole textbook again.

8. What are some real-life examples that help to memorise the difference between direct and inverse proportions?

Thinking of real-life examples is an excellent revision technique.

  • For Direct Proportion: The more money you save per month, the more you save in a year (both increase).
  • For Inverse Proportion: The higher the speed of a car, the less time it takes to cover a fixed distance (one increases, the other decreases).