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CBSE Notes
Class 8
Maths
Chapter 11 Direct and Inverse Proportions

CBSE Notes Class 8 Maths Chapter 11 Direct and Inverse Proportions

1.0Introduction to Proportions 

The relationship between 2 quantities where one quantity changes with another quantity is known as proportions. These are of two types - 

  • Direct proportions
  • Inverse proportions

A proportion is written as: 

ba​=dc​

This means the ratio of a & b is equal to the ratio of c & d in simple terms. 

2.0Download CBSE Class 8 Maths Chapter 11 Direct and Inverse Proportions Notes: Free PDF

Download the free PDF of CBSE Notes Class 8 Maths Chapter 11 Direct and Inverse Proportions to understand key concepts, formulas, and real-life applications. These notes are concise, easy to follow, and great for quick revision and exam preparation.

Class 8 Maths Chapter 11 Revision Notes:

3.0CBSE Class 8 Maths Chapter 11 Direct and Inverse Proportions - Revision Notes

Direct Proportions 

If two quantities are in proportion, and if one quantity increases, the other also increases, or if one decreases, the other also decreases, then the two quantities are said to be in direct proportions. It can be mathematically represented as: 

yx​=ba​ Or x∝y

This means x is directly proportional to y. 

Key Point: In direct proportion, the ratio of two quantities always remains constant. 

If x1​∝y1​ and x2​∝y2​, then y1​x1​​=y2​x2​​

Formula: x=k⋅y

Here, k is the constant of proportionality. 

Example: 

Suppose a car is traveling at a constant speed, and it takes 2 hours to reach a distance of 60 km. Now, the same car travels for 3 hours, and the speed of the car remains constant. What will the distance be that it will cover?

Solution: 

Let the time taken by the car be x and the distance travelled be y. 

Here, we can see as the value of x increases, the value of y also increases in such a way that xy does not change (K)

In this example, 

260​=3y​

y=260×3​

y = 90

Here, the ratio is constant, that is, 30/1. 

Example: 

The variable x is directly proportional to y. If x increases by p%, then by what percent will y increase?

Solution: 

According to question 

x∝y

The new value of x = x  + x(p/100)

=x(100100+p​)

It is given that, x = y 

Hence, y=y(100100+p​)

So, y also increases by p%. 

Memory Tip: “Same Direction”

  • In other words, it's like "both move in the same direction." If one goes up, the other will, too.
  • Imagine it like a straight line: In maths, when you draw a graph, the lines will always rise or fall together.

Inverse Proportions 

If two quantities are in proportion, and if one quantity increases and the other one decreases, and vice-versa, then this type of proportion is known as inverse proportion. The mathematical representation of inversely proportional quantities is as follows. 

x∝y1​

This means x is inversely proportional to y. 

Key Point: In inverse proportions, the product of both quantities remains constant. 

x1​⋅y1​=x2​⋅y2​

Formula: x⋅y=k

Where k is the constant of proportionality.

Example: 

Six pipes are required to fill a tank in 1 hour. How many pipes will be used if the time taken by the tank is 2 hours?

Solution: 

Let the time taken by the pipes be x. The number of pipes be y. 

Here, we can see that as the number of pipes decreases, the time taken to fill the tank also increases in such a way that the product of x and y remains constant.  

In the given example,

6×1=2×x

x=6÷2

x=3

Hence, the number of pipes used is 3. In the following example, the product's two quantities remain the same, which is 6. 

Example: 

A car covers a distance in 40 minutes with an average speed of 60 km/h. What should be the average speed to cover the same distance in 25 minutes?

Solution: 

Let the distance covered be = x 

Converting minutes into hours = 40/60 = 2/3

We know the formula for speed is 

Speed=TimeDistance covered​

Let’s find the distance covered with the help of this formula 

60=32​x​

x = 60 x 2/3 = 40 km

Hence, speed for 25minutes or (5/12) hour

Speed = 40/(5/12) = 84 km/h

Also Read: Direct and Inverse Proportions

Memory Tip: Opposite directions 

  • In common words, "where one goes up, so the other goes down." That is, an increase of one diminishes that of the other.
  • Just imagine a car’s speed and time: When the speed increases, then the time taken by the car to reach a certain distance decreases. 

4.0Key Features of CBSE Maths Notes of Class 8 Chapter 11

  • The notes include memory tips at the end of each section for easy understanding of the concepts. 
  • The notes are designed to make it easy for students to read and learn easily, making it ideal for self-learning. 
  • These notes are aligned with the latest CBSE curriculum.

Chapter-wise CBSE Notes for Class 8 Maths:

Class 8 Maths Chapter 1 - Rational Numbers Notes

Class 8 Maths Chapter 2 - Linear Equations In One Variable Notes

Class 8 Maths Chapter 3 - Understanding Quadrilaterals Notes

Class 8 Maths Chapter 4 - Data Handling Notes

Class 8 Maths Chapter 5 - Squares and Square Roots Notes

Class 8 Maths Chapter 6 - Cubes and Cube Roots Notes

Class 8 Maths Chapter 7 - Comparing Quantities Notes

Class 8 Maths Chapter 8 - Algebraic Expressions and Identities Notes

Class 8 Maths Chapter 9 - Mensuration Notes

Class 8 Maths Chapter 10 - Exponents and Powers Notes

Class 8 Maths Chapter 11 - Direct and Inverse Proportions Notes

Class 8 Maths Chapter 12 - Factorisation Notes

Class 8 Maths Chapter 13 - Introduction to Graphs Notes


Chapter-wise NCERT Solutions for Class 8 Maths All Chapters:-

Chapter 1: Rational Numbers

Chapter 2: Linear Equations in One Variable

Chapter 3: Understanding Quadrilaterals

Chapter 4: Data Handling

Chapter 5: Squares and Square Roots

Chapter 6: Cubes and Cube Roots

Chapter 7: Comparing Quantities

Chapter 8: Algebraic Expressions and Identities

Chapter 9: Mensuration

Chapter 10: Exponents and Powers

Chapter 11: Direct and Inverse Proportions

Chapter 12: Factorisation

Chapter 13: Introduction to Graphs

Frequently Asked Questions

If both quantities increase or decrease at the same time, then they are directly proportional. And if one quantity increases while the other decreases, then it is inversely proportional to quantity.

The constant of proportionality (k) is a constant value that may be used to express a relation of two quantities in proportion, helping to outline their relation.

Sometimes, a problem will involve both direct and inverse proportions. You use the appropriate formula to solve each part.

They help in solving real-world problems like speed, time, distance, and costs.

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