NCERT Class 8 Mathematics Mathematics: Chapter 11 — Direct and Inverse Proportions
This chapter introduces the concepts of direct and inverse proportions, fundamental to understanding variations in quantities. It begins with relatable scenarios like preparing tea or arranging chairs, illustrating how changes in one quantity affect another. The chapter defines direct proportion with examples such as the relationship between the weight of sugar and its cost, or petrol consumption and distance traveled. It explains that in direct proportion, as one quantity increases, the other increases proportionally, maintaining a constant ratio (x/y = k). This concept is crucial for solving real-world problems involving proportional relationships, forming a key part of the Class 8 Mathematics curriculum for CBSE students.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 11 — Direct and Inverse Proportions |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 2 minutes |
| Word count | 348 |
Learning outcomes
- Understand the concept of direct proportion.
- Identify real-world situations involving direct proportion.
- Solve problems using the relationship of direct proportion (x/y = k).
- Differentiate between direct and inverse proportional relationships.
Vocabulary
| Word | Meaning |
|---|---|
| Proportion | A relationship where two quantities change together in a specific way. |
| Direct Proportion | A relationship where an increase in one quantity causes a proportional increase in another quantity. |
| Constant Ratio | The ratio between two quantities in direct proportion remains unchanged. |
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Practice questions
- If 5 kg of sugar costs ₹180, what is the cost of 8 kg of sugar? Answer: ₹288
- A car travels 180 km on 12 litres of petrol. How far will it travel on 20 litres of petrol? Answer: 300 km
- If the cost of 10 pens is ₹150, what is the cost of 7 pens? Answer: ₹105
Frequently asked questions
What is direct proportion?
Direct proportion is a relationship where if one quantity increases, the other quantity increases by the same factor, and vice versa. Their ratio remains constant.
How can we identify direct proportion?
We can identify direct proportion by checking if the ratio between corresponding values of the two quantities remains constant (x/y = k).
Give an example of direct proportion.
The cost of sugar and its weight are in direct proportion. If you buy more sugar, the cost increases proportionally.
What is the formula for direct proportion?
If x and y are in direct proportion, then x/y = k, where k is a constant. This can also be written as x1/y1 = x2/y2.
How does speed relate to distance traveled with a fixed amount of fuel?
For a fixed amount of fuel, the distance traveled is directly proportional to the speed. If you travel faster, you cover more distance in the same amount of fuel.
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Topics covered
NCERT Class 8 Mathematics — Mathematics — Chapter 11 — Direct and Inverse Proportions. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.