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RS Aggarwal Solutions

RS Aggarwal Class 8 Mathematics Solutions for Chapter-12 Direct and Inverse Proportions

RS Aggarwal Class 8 Mathematics Solutions for Chapter-12 Direct and Inverse Proportions

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Class 8 RS Aggarwal Maths Direct and Inverse Proportions Solutions - Free PDF Download

After learning ratio and proportion in the previous classes, you will proceed to learn direct and indirect or inverse proportion in Class 8. RS Aggarwal Class 8 Maths Chapter 12 will teach the students the different concepts of proportions and how to use them to solve the questions. These concepts will be clarified by using examples and then your skills will be assessed in the exercises.

Use RS Aggarwal Class 8 Chapter 12 solution to solve all these questions in the right format and learn the easiest methods. Refer to the solution file to discover the best approaches and practice solving these questions. You can download this file and use it offline at your convenience.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Download Class 8 Maths and Class 8 Science NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Direct and Inverse Proportion: An Overview

Inverse Proportion- When the value of a variable falls or grows in proportion to the value of another variable, we can say that the variables are in inverse proportion.

Direct Proportion- If the value of a variable x always rises or falls in lockstep with the rise or fall in the value of variable y, the variables x and y are said to be in direct proportion.

Mathematically, any two varying physical values are said to be proportional if they are multiplicatively related by a constant term. The more we eat, for example, the more energy we obtain, and the more we run, the more energy we lose.

Elaborate study material, solutions to several problems, revision notes, sample papers, and previous years’ question papers which have been made available by Vedantu are very helpful resources for the students.

RS Aggarwal Class 8 Maths Chapter- 13 Direct and Inverse Proportions Solutions is easily accessed online in PDF format for students, these are available along with solved answers on both Vedantu’s site and app.
Vedantu aims to ensure students have the right study material to learn every chapter thoroughly and help them to score better.
Vedantu RS Aggarwal Solutions are the best source for the final practice for the final exams.

Important Formulae

Direct Proportion: Two quantities x and y are said to be in direct proportion their corresponding values grow (drop) in such a way that their ratio remains constant. If x/y=k (where k is a positive value), x and y are said to vary directly. If y1, y2 are the values of y that correspond to the values x1, x of x, respectively, x1/y1 = x2/y2.
Inverse Proportion: Two quantities x and y are said to be in inverse proportion if a rise in x induces a proportional decrease in y (and vice versa) in such a way that their product remains constant. If x/y = k, then x and y are said to vary in opposite directions. If y1, y2 are the values of y that correspond to the values of x1, x2 respectively, then x1, Y1 = x2, y2 or x1y1x1y1 = x2y2

Direct and Inverse Proportions: RS Aggarwal Class 8 Maths Chapter 12 Solution Summary

Class 8 is the base of mathematics if you consider the chapters and the syllabus of the higher classes. Hence, studying mathematics in this class properly is a crucial factor. To make your preparations stronger, you need to follow the stepwise methods and approaches used by the teachers to solve the problems of RS Aggarwal Class 8 Maths Chapter 12. Let us check what you can get and benefit from using its solution.

In the first exercise, you will find problems related to simple proportions where you will have to find the value of an unknown section using the concepts. The preliminary problems are a recapitulation method used by the author. You will find out the relation between the known and unknown quantities in the questions by using these concepts. These arithmetic questions are lengthy. Make sure you use the RS Aggarwal Class 8 solutions Maths Chapter 12 while practising these exercises to find the right way to solve these questions without wasting your time.

On proceeding further, you will learn how to use these concepts of Direct and Inverse Proportions in calculating distance, cost, time, etc by using the hints in the problems. As mentioned earlier, forming the respective sentences in this chapter is a challenge too. Consider the format used by the experts following the NCERT guidelines. This format will help you write precisely and concisely to solve the questions. Use the RS Aggarwal solutions Class 8 Maths Ch 12 to get an idea of how these complex questions can be approached and solved in no time.

The more you proceed in this exercise; you will find that the difficulty level of the questions is increasing. Every question will require a strong conceptual base to solve. You will have to be very intuitive in solving these questions. The calculations are easier but formatting the answer is tough. Practice answering such questions using the solution for RS Aggarwal Class 8 Maths Direct and Inverse Proportion so that you can make immense progress in very little time and complete this chapter faster.

The next exercise will concentrate on the problems related to inverse proportionality. The author has segregated the problems into two major exercises for the benefit of students. In this part, you will discover the challenges of solving questions related to inverse proportions. Here, you will learn the difference between Direct and Inverse Proportion in a better way. Check out the solutions of Direct and Inverse Proportion Class 8 RS Aggarwal questions to grab the concept even better. Learn how to use them to solve critical questions without any hassle.

All the Exercise questions with solutions in Chapter-12 Direct and Inverse Proportions are given below:

Exercise (Ex 12A) 12.1

Exercise (Ex 12B) 12.2

Exercise (Ex 12C) 12.3

Tips to Prepare Class 8 RS Aggarwal Chapter 12 Direct and Inverse Proportions

The biggest challenge in this section is to keep the concepts of direct proportion aside and use the exact opposite concepts of inverse proportion. Do not get confused and let the RS Aggarwal Class 8 Chapter 12 solution simplify your way into this chapter.

Concentrate on the approaches designed by the teachers to identify and differentiate between Direct and Inverse Proportion easily. Use your common sense to understand which one of them fits into the description of the problem. This is how you can prepare RS Aggarwal solutions Class 8 Chapter 12. Download its solution and utilize your time efficiently.

FAQs on RS Aggarwal Class 8 Mathematics Solutions for Chapter-12 Direct and Inverse Proportions

1. Where can I find complete and accurate solutions for RS Aggarwal Class 8 Maths Chapter 12, Direct and Inverse Proportions?

You can access the complete, step-by-step solutions for all exercises in RS Aggarwal Class 8 Maths Chapter 12 on this page. Our subject experts have solved every question from Exercises 12A, 12B, and 12C, ensuring each solution follows the correct methodology as per the latest CBSE 2025-26 guidelines.

2. What are the key topics covered in the solutions for RS Aggarwal Class 8 Chapter 12?

The solutions for Chapter 12, Direct and Inverse Proportions, provide detailed methods for understanding and solving problems related to:

Identifying quantities in direct proportion and using the formula x₁/y₁ = x₂/y₂.
Recognising quantities in inverse proportion and applying the formula x₁y₁ = x₂y₂.
Solving practical word problems based on speed-distance-time, time-work, and cost-quantity scenarios.
Distinguishing between the two types of variations to select the correct problem-solving approach.

3. How do I identify whether a word problem involves direct or inverse proportion?

To correctly identify the relationship, analyse how the two quantities behave together.

It is a direct proportion if an increase in one quantity causes a proportional increase in the other (e.g., more items purchased leads to a higher total cost).
It is an inverse proportion if an increase in one quantity causes a proportional decrease in the other (e.g., increasing the speed of a vehicle reduces the time taken to cover a fixed distance).

Always establish this core relationship before applying a formula.

4. What is the fundamental difference between the formulas used for direct proportion (x/y = k) and inverse proportion (xy = k)?

The fundamental difference lies in the constant value 'k' that defines the relationship:

For direct proportion, the ratio of the two variables (x and y) is constant. The formula is x/y = k, or more commonly for problem-solving, x₁/y₁ = x₂/y₂.
For inverse proportion, the product of the two variables is constant. The formula is x × y = k, which leads to the problem-solving equation x₁y₁ = x₂y₂.

Understanding this distinction is key to solving problems from this chapter correctly.

5. Why is it important to use the correct step-by-step method shown in the RS Aggarwal solutions for exams?

Using the correct step-by-step method is critical for scoring full marks in exams. As per the CBSE evaluation process, marks are often awarded for each logical step, not just the final answer. A complete solution demonstrates your understanding and should include:

Identifying the given quantities.
Stating whether the proportion is direct or inverse.
Writing the correct formula.
Showing accurate calculations.
Concluding with the final answer and appropriate units.

6. Which exercises in RS Aggarwal Class 8 Chapter 12 are considered most important for exams?

While all exercises are important for building a strong foundation, students often find the application-based word problems in Exercise 12B and 12C to be particularly crucial. These questions test the ability to apply the concepts of inverse proportion to real-world scenarios like 'time and work' or 'provisions for a garrison', which are common in examinations.

7. What are some common mistakes to avoid when solving problems on direct and inverse proportions?

A common mistake is incorrectly identifying the type of proportion. Students sometimes apply the direct proportion formula to an inverse proportion problem, or vice-versa. Another frequent error is mixing up the values (e.g., swapping x₂ and y₂). To avoid this, always write down the variables clearly (e.g., let 'x' be the number of workers and 'y' be the time taken) and double-check the relationship before calculating.