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RS Aggarwal Class 8 Chapter 12 Solutions (Direct And Inverse Proportions)

RS Aggarwal Class 8 Maths Solutions for Chapter 12 ‘Direct and Inverse Proportions’ can help you understand the tough concepts of this chapter easily. The exercise questions in this chapter of RS Aggarwal Class 8 Maths Solutions are based on calculating direct and inverse proportions and their real-life applications. After practising these exercises, you will be able to solve all kinds of questions related to this topic in your exams. 

Chapter 12 ‘Direct and Inverse Proportions’ contains 3 exercises and 40 questions of varying difficulty levels. These questions are based on the latest CBSE Class 8 Maths syllabus. The chapter also contains higher-order thinking questions that would prepare you for competitive exams and olympiads. You must read the important topics of the chapter given below to revise the chapter. 

The subject matter experts at Instasolv have prepared step-by-step solutions to all the exercises of Chapter 12 of RS Aggarwal Class 8 Maths book. These solutions will be your guide if you have any confusion in the chapter. You can now easily identify your mistakes and prepare this chapter well for your exams. 

Important Topics for RS Aggarwal Class 8 Maths Solutions Chapter 12: Direct and Inverse Proportions 

Variation

  • There are times when two quantities are related to each other in such a way that their presence or absence can affect each other. 
  • For example, there are 200 plates in a kitchen and it takes 5 people to clean them in 20 minutes. 
  • However, if there were 10 people, it would take 10 minutes to clear those plates.
  • Here, you can see that time taken and the number of people is related to each other. 
  • As the number of people increases, the time is taken decreases. 
  • This is the concept of variation. 

Direct Proportion

  • Direct proportion is a way of expressing the variation between two things or two quantities. 
  • For example, a car can travel 100 kilometres with 10 litres of petrol. 
  • However, with 20 litres of petrol, the car would travel 200 kilometres and with 30 litres of petrol, the car would travel 300 kilometres. 
  • Here, you can see that as the amount of petrol is increasing, so is the amount of distance travelled. 
  • So, we can say that the amount of petrol and distance travelled are in direct proportion. If one quantity increases so is the other. 
  • In cases where an increase in one quantity leads to an increase in the other quantity, such quantities are called to be in direct proportion.

Inverse Proportion 

  • Inverse proportion is another way of expressing the variation between two things or two quantities.
  • For example, a tank can be filled with water in 20 minutes with 6 pipes. 
  • However, if there are 10 pipes, it takes only 10 minutes to fill the tank and if there are 12 pipes, it takes only 8 minutes to fill the tank. 
  • Here, you can see that as the number of pipes is increasing, the time is decreasing. 
  • In such cases, where an increase in one quantity leads to a decrease in the other quantity, such quantities are called to be in inverse proportion. 

Identifying Inverse or Direct Proportion

Let us take an example here. Suppose, there is a hostel that can accommodate 200 students for 20 days. Now, we need to find how long the hostel will be able to accommodate the students if 200 more students are asking for accommodations. 

To solve this problem, we need to arrange the given data as: 

Number of Students  200 400
Number of Days  20 d

From this table, we can easily judge that as the number of students has increased the number of days would decrease. So this is a case of inverse proportion. Now, the number of days can be calculated as:

200 x 20 = 400 x d 

200 x 20 / 400 = d 

d = 10 days. 

Exercise Discussion for RS Aggarwal Class 8 Maths Solutions Chapter 12: Direct and Inverse Proportions

  • Exercise 12A contains 15 questions, Exercise 12B has 15 questions and Exercise 12C has 10 questions. 
  • In all these exercises, there are similar kinds of questions just to ensure that you get enough practice of the concepts. 
  • At first, there are questions where you have to identify if the given values are inversely proportional or directly proportional. 
  • There are also some word problems related to inverse and direct proportions where you are given some relationships between the quantities, you have to identify whether they are inversely proportional or directly proportional and then, you have to find the missing values. 
  • Some of the word problems of the chapter might appear tricky to you as you need to understand the language of the question correctly. This is where our RS Aggarwal Solutions for Class 8 Maths Chapter 12 would help you. We have provided clear explanations for all the word problem questions. 

Benefits of RS Aggarwal Class 8 Maths Solutions Chapter 12: Direct and Inverse Proportions by Instasolv

  • Solving questions related to inverse and direct proportions is now super easy with our RS Aggarwal Solutions for Class 8 Maths Chapter 12. These solutions are prepared by the best maths teachers in India. 
  • All the solutions are as per the latest CBSE exam pattern for Class 8. 
  • The explanations are easy to understand. Our experts have specifically used simple language ensuring the aptitude of a Class 8 student. 
  • The solutions are regularly updated as per the changes in the syllabus.