Direct & Inverse Proportions Class 8 NCERT Guide

Have you ever noticed how buying more items increases your total bill, but increasing speed reduces the time taken to travel the same distance? These everyday situations are not random. They follow a clear mathematical relationship called direct and inverse proportion.

This Class 8 chapter from NCERT helps you understand how two quantities are connected. Once you grasp this concept, solving real life problems becomes much easier. In this blog, you will learn the complete NCERT concept in simple language along with a wide range of practice questions. As requested, only questions are provided so that you can practice on your own.

What is Proportion in Class 8

Before understanding direct and inverse proportion, let us first understand what proportion means.

A proportion is an equality of two ratios. When two ratios are equal, they are said to be in proportion.

For example
2 divided by 4 is equal to 3 divided by 6

This means the ratios are in proportion.

In Class 8, NCERT focuses on how two quantities change in relation to each other.

Direct Proportion Class 8 Concept

Definition in Simple Words

Two quantities are said to be in direct proportion when both increase together or both decrease together.

If one value becomes larger, the other also becomes larger. If one becomes smaller, the other also becomes smaller.

Real Life Examples of Direct Proportion

When you buy more items, you pay more money
When you work more hours, you earn more salary
When distance increases at constant speed, time also increases

Mathematical Representation

If two quantities x and y are in direct proportion, then

x divided by y is constant

or

y is equal to k multiplied by x

where k is a constant value

How to Identify Direct Proportion

Check whether both quantities are moving in the same direction. If yes, then it is a direct proportion.

Inverse Proportion Class 8 Concept

Definition in Simple Words

Two quantities are said to be in inverse proportion when one increases and the other decreases.

If one value becomes larger, the other becomes smaller.

Real Life Examples of Inverse Proportion

More workers take less time to complete work
Higher speed reduces travel time
More taps fill a tank faster

Mathematical Representation

If two quantities x and y are in inverse proportion, then

x multiplied by y is constant

or

y is equal to k divided by x

How to Identify Inverse Proportion

Check whether one quantity increases while the other decreases. If yes, then it is an inverse proportion.

Difference Between Direct and Inverse Proportion

In direct proportion both quantities move in the same direction. In inverse proportion they move in opposite directions.

In direct proportion the ratio remains constant. In inverse proportion the product remains constant.

Direct proportion follows y equals kx. Inverse proportion follows y equals k divided by x.

Graph Understanding for Class 8

In direct proportion, the graph is a straight line passing through the origin.

In inverse proportion, the graph is a curve.

This helps students visually understand the relationship between quantities.

Important Formulas for Revision

For direct proportion
x1 divided by y1 is equal to x2 divided by y2

For inverse proportion
x1 multiplied by y1 is equal to x2 multiplied by y2

Practice Questions Direct Proportion Class 8

Basic Questions

1. If 4 notebooks cost 80 rupees, what will be the cost of 10 notebooks

2. A car travels 50 kilometres in 2 hours. How far will it travel in 6 hours at the same speed

3. If 6 pens cost 48 rupees, find the cost of 20 pens

4. 10 workers earn 2000 rupees in a day. How much will 25 workers earn

5. If 5 metres of cloth cost 250 rupees, what is the cost of 15 metres

Make maths easier and more fun with expert-led learning designed for Class 8 students. Strengthen concepts like direct and inverse proportion with guided practice.
Explore our Maths  programs to boost academic skills.

Intermediate Questions

6. A train covers 120 kilometres in 3 hours. How much distance will it cover in 8 hours

7. If 8 books weigh 2 kilograms, what will be the weight of 20 books

8. A machine produces 150 units in 5 hours. How many units will it produce in 12 hours

9. If 4 litres of milk cost 200 rupees, what is the cost of 10 litres

10. If 9 pencils cost 45 rupees, find the cost of 30 pencils

Word Problems

11. The cost of 12 apples is 240 rupees. What will be the cost of 25 apples

12. A person earns 3000 rupees in 6 days. How much will he earn in 15 days

13. A bike travels 240 kilometres using 8 litres of petrol. How far will it travel using 15 litres

14. A school collects 500 rupees from each student. What will be the total amount if there are 600 students

15. A worker makes 18 tables in 6 days. How many tables will he make in 15 days

Practice Questions Inverse Proportion Class 8

Basic Questions

16. 8 workers complete a work in 10 days. How many days will 4 workers take

17. A car takes 5 hours at 60 kilometres per hour. How much time will it take at 120 kilometres per hour

18. 10 men can do a job in 12 days. How many days will 5 men take

19. A tank is filled in 6 hours by 3 pipes. How long will it take with 1 pipe

20. If 12 workers take 8 days, how many days will 24 workers take

Struggling with proportions or word problems? Get step-by-step guidance and improve your confidence in solving real exam-level questions.
Join our Maths program to excel in studies and express ideas clearly.

Intermediate Questions

21. A group of 20 workers can complete work in 15 days. How long will 10 workers take

22. If 16 men can finish a project in 12 days, how many days will 24 men take

23. A car completes a journey in 6 hours at 80 kilometres per hour. How long will it take at 40 kilometres per hour

24. 5 machines complete a task in 10 hours. How long will 2 machines take

25. If 9 pipes fill a tank in 6 hours, how long will 3 pipes take

Word Problems

26. A team of 6 people completes a task in 18 days. How long will 9 people take

27. If 15 men can do a job in 10 days, how many days will 5 men take

28. A train takes 4 hours at 90 kilometres per hour. How long will it take at 45 kilometres per hour

29. 18 workers build a wall in 9 days. How long will 6 workers take

30. If 8 taps fill a tank in 4 hours, how long will 4 taps take

Mixed Practice Questions

31. Identify whether the following are direct or inverse proportion
    Number of books and total cost
    Speed and time
    Number of workers and days
    Distance and fuel used

32. A car travels 200 kilometres in 4 hours
    Find the distance in 10 hours at the same speed
    Find the time taken to travel 200 kilometres at double speed

33. 12 workers complete work in 15 days
    How many days will 6 workers take
    How many workers are needed to complete the work in 5 days

34. If 10 pens cost 100 rupees
    Find the cost of 25 pens
    If the cost remains 100 rupees, how many pens can be bought if price is reduced

35. A tank is filled by 4 pipes in 12 hours
    Time taken by 2 pipes
    Number of pipes needed to fill in 6 hours

Higher Order Thinking Questions

36. A contractor hires workers to complete work in a fixed number of days. If more workers are added, what happens to the time required and what type of proportion is this

37. A cyclist reduces speed due to heavy traffic. What happens to the time taken and what is the relationship

38. A shopkeeper gives discounts on bulk buying. Is the relationship between quantity and price always direct. Think and explain

39. Can two quantities show both direct and inverse proportion at the same time. Give reasoning

40. Think of a real life example where both direct and inverse proportion are applied together

Common Mistakes Students Should Avoid

Students often confuse direct and inverse proportion because they do not check the direction of change carefully.

Another common mistake is using the wrong formula without understanding the relationship.

Ignoring units and rushing through word problems also leads to errors.

Tips to Master This Chapter

First understand whether the quantities move in the same or opposite direction.

Write the given data clearly before solving.

Practice different types of questions regularly.

Focus more on understanding rather than memorizing formulas.

Join PlanetSpark’s Learning Programs for Maths and Communication Skills

When it comes to mastering concepts like direct and inverse proportion in Class 8, students often need more than just textbook learning. They need structured guidance, regular practice, and the confidence to approach problem-solving with clarity.

Why Choose PlanetSpark

1. Strong focus on concept clarity with step-by-step teaching

2. Personalized learning plans based on student level

3. Regular practice sessions with exam-oriented questions

4. Expert mentors who simplify complex topics

5. Improves problem-solving and logical thinking

6. Builds confidence through Public Speaking programs

7. Helps students perform better in school and beyond

Conclusion

The chapter direct and inverse proportion in Class 8 is simple if you connect it with real life situations. Instead of relying only on formulas, try to understand how quantities behave.

You can always use NCERT PDFs and tools like GPT to simplify learning, but real improvement comes from practice. Go through these questions carefully and try solving them on your own to build confidence.

If you want, I can also create a test paper or worksheet based on this chapter for revision.