Sets in Mathematics are the collection of definite objects that can form a group. The collection of numbers, days of the week, types of vehicles,...

Sets

April 11, 2024**Exercise 13.1 Class 8 Maths NCERT Solutions:** In this article we have provided the NCERT Solutions for Class 8 Maths Chapter 13 exercise 13.1. The NCERT Solutions on Maths Class 8 are valuable resources that students can refer to, to score good marks in their exams. These NCERT Solutions are up-to-date and they have been devised as per the latest CBSE guidelines.

Embibe’s NCERT Solutions for Class 8 Mathematics Chapter 13 Exercise 13.1 includes, updated, easily understandable, and comprehensive information for students that they can rely on. Students should practice the questions given within the NCERT solutions of the chapter to score good marks in their CBSE Class 8 Maths exams. We have provided the NCERT solutions for Class 8 Chapter 13 Exercise 13.1 Maths in the PDF format. This will enable students to download the chapter and study it offline. Students can continue to read further to know more on the solutions in this chapter.

We have provided the **NCERT Class 8 Maths Solutions** in PDF format so that Class 8 students find it easy to study the chapter offline. Embibe experts have devised the solutions for Direct and Inverse Proportions as per the latest CBSE guidelines. Here below, we have provided a brief overview of the NCERT Solutions for Direct and Inverse Proportions chapter so that students find it easy to refer:

Class | Class 8 |

Chapter Name | Direct and Inverse Proportions |

Exercise Number | Exercise 13.1 |

Topic Name | Introduction |

Language | English |

Solution Type | In-text Solved Questions |

Official Website | https://ncert.nic.in/ |

Students can refer to the Class 8 Maths Chapter 13 Exercise 13.1 Solutions. Studying and practicing all the in-text questions provided in the NCERT textbooks will help them to effectively prepare for their CBSE Class 8 school examinations and final examinations. It will help them get a fair understanding of all the concepts covered in the NCERT books.

Students can start studying from the **NCERT Solutions for Class 8 Maths Chapter 13 Exercise 13.1**. They can refer to the study materials online or download the PDFs and refer to the materials offline at any place at their own convenience In this article we have provided the NCERT Solutions on Maths Class 8 Chapter 13 Exercise 13.1** **for the easy reference of the students. They can choose to bookmark these solutions to study them later.

**NCERT Class 8 Maths Chapter 13 Exercise 13.1 PDF**

NCERT Class 8 Maths Chapter 13 Exercise 13.1 introduces the students to the concept of Direct and Inverse proportions. In Maths Class 8 Chapter 13 Exercise 13.1, students will deal with multiple integers in a sum. They will learn how a pair of integers or variables represented in the form of a ratio, is related to another pair of integers or variables, which is also represented in the form of a ratio.

**Q.1: Following are the car parking charges near a railway station up to**

4 hours | Rs. 60 |

8 hours | Rs. 100 |

12 hours | Rs. 140 |

24 hours | Rs. 180 |

Check if the parking charges are in direct proportion to the parking time.

**Solution:** Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

If y1, y2 are the values of y corresponding to the values x1, x2 of x respectively, then x1y1=x2y2.

Here, 604=15, 1008=252, 14012=353, 18024=152

460≠8100≠12140≠24180

Hence, the parking charges are not directly proportional to the parking time.

**Q.2: A loaded truck travels 14 km in 25 minutes. If the speed remains the same, it can travel k km in 5 hours, then find the value of k.**

**Solution: **Given that the distance travelled by the truck in 5 hours is k km.

We know, 1 hour=60 minutes.

So, 5 hours=5×60=300 minutes.

The given information can be tabulated as follows:

Distance travelled (in km) | 14 | k |

Time (in min) | 25 | 300 |

By, keeping the speed constant, we have distance travelled by a vehicle is directly proportional to the time taken by the vehicle. If x and y are two quantities in direct proportion, then x1y1=x2y2. We have, 1425=k300 k=14×30025=420025=168

Therefore, the truck will travel 168 km in 5 hours.

Hence, the value of k is 168.

**Q.3: A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of the base. In the following table, the parts of the base that need to be added is given. Find a+b+c+d.**

Parts of Pigment | 1 | 4 | 7 | 12 | 20 |

Parts of base | 8 | a | b | c | d |

**Solution: **Given table:

Parts of Pigment | 1 | 4 | 7 | 12 | 20 |

Parts of base | 8 | a | b | c | d |

Let us assume the parts of red pigment to be x and the parts of base to be y. Given that the paint is prepared by mixing 1 part of red pigments with 8 parts of base. The quantity of red pigment will increase with increase in base quantity. So, it is a direct proportion. Therefore, we have, 18=4a=7b=12c=20d ∴ 18=4a⇒a=32 Similarly, 18=7b⇒b=56 18=12c⇒c=96 18=20d⇒d=160 Therefore, a+b+c+d=32+56+96+160=344.

**Q.4: **A mixture of paint is prepared by mixing some parts of red pigments with some parts of base. If 1 part of a red pigment requires 75 ml of base, how much red pigment(in ml) should we mix with 1800 ml of base?

**Solution:** Let us assume the quantity of red pigment to be mixed with1800 ml of base to be x.

Parts of red pigment | 1 | x |

Parts of base(in ml) | 75 | 1800 |

Since these quantities are in direct proportion, the value of x can be found as,175=x1800

x=1×180075=24

Therefore, 24 ml red pigment we should mix with 1800 ml of base.

**Practice 8th CBSE Exam Questions**

NCERT Solutions for Class 8 Maths helps the students effectively grasp a concept. Our subject matter experts at Embibe have found the best possible ways to solve a sum and present the same in this chapter. This helps the students to easily apply these concepts to sums that are of a similar kind. Students who find the concepts provided in these solutions helpful, not only are prepared for their school exams but also competitive exams, such as Olympiads. Students who understand these concepts given in the CBSE Class 8 Maths syllabus, are able to apply their practical and theoretical knowledge to real-life scenarios.

Chapter 13 Maths Class 8 covers the essential topics on Direct and Inverse proportions that CBSE Class 8 students will have to study as a part of their Maths syllabus. Students who have studied Chapter 13 Maths Class 8 syllabus, will be able to answer different types of questions based on direct proportion and inverse proportion. They will be able to determine the value of quantities following the relation of direct and Inverse proportion.

Studying from Embibe’s Class 8 Maths Exercise 13.1 NCERT Solutions, comes with numerous advantages. Here, we have provided some of the advantages of studying from Embibe’s NCERT solutions:

- Embibe’s Exercise 13.1 Class 8 Maths and its NCERT solutions is up-to-date with the the latest CBSE guidelines.
- The Maths Class 8 NCERT solutions at Embibe are prepared by our best subject matter experts. The experts have explained the concepts of all the chapters covering the Class 8 Maths syllabus in a language that a Class 8 student finds to understand.
- The experts have elaborated on the concepts. This way the students are able to understand the factual information efficiently and solve the sums in Exercise 13.1 Class 8 Maths syllabus.
- These solutions on Exercise 13.1 Class 8 Maths are provided to students. In this way, students can access the study the materials online. Alternatively, they can download the PDFs of these chapters and study them wherever they want.
- The Class 8 Maths NCERT solutions provides a wide coverage on all the types of questions listed in the CBSE textbooks.
- The NCERT solutions by Embibe covers numerous types of questions which help the students to prepare for their exams effectively and in a comprehensive manner. Numerous examples are covered in the chapter, on the various kinds of questions that students might be asked in the exam such as MCQs, short questions, long questions, etc. This is what helps the students to effectively prepare for their exams.
- Students who do not have any doubt in understanding the concepts from the Embibe’s NCERT solutions on Maths Class 8 Chapter 13 Exercise 13.1 are able to complete their homework on time. They can also effectively prepare for their exams.
- The subject matter experts at Embibe have prepared the Class 8 Math Chapter 13 NCERT solutions in a manner such that students are able to prepare their lessons effectively for their exams.
- The Embibe subject matter experts have derived the solutions in Exercise 13.1 Class 8 Maths of the NCERT Maths books following a step-by-step approach. This has helped the beginners to the chapter in understanding the manner in which they should solve a certain sum or problem.
- Our experts have covered the chapters in totality, presenting the concepts in a comprehensive manner. They have ensured that no topic or concept of the NCERT textbooks is left out.

Given below are some of the commonly asked questions on CBSE Chapter 13 Maths Class 8 syllabus:

**Q.1: What does NCERT Solutions on Class 8 Maths Chapter 13 deal with?****Ans:** The NCERT Solutions on Class 8 Maths Chapter 13 provides the concept of Direct and Inverse Proportions to the Class 8 students of the CBSE Board.

**Q.2. What can I learn from Exercise 13.1 of the Class 8 Maths syllabus?****Ans: **In Exercise 13.1 of the Class 8 Maths syllabus, students will learn to calculate proportions between two different quantities, proportions between different parts of a base, solve real-life situations such as comparing parking charges with the number of hours, etc.

**Q.3: What are some examples of direct proportion?****Ans: **Some of the examples of direct proportion are as follows:

- The number of fruit is directly proportional to the price of fruit.
- The number of products in sale, is directly proportional to the profit
- The number of work hours is directly proportional to the salary paid
- Distance travelled is directly proportional to time.

**Q.4: What are some of the real-life examples of Inverse proportion?****Ans:** Some examples of inverse proportion are as follows:

- When the speed of the car increases, the time taken to reach the destination decreases.
- The more the number of children at a birthday party, the smaller is the share of cake that they receive.
- When there are more cars, there is less space on the road.

**Q.5: Is there any place where I can practice questions on Direct and Inverse Proportions?Ans: **Students can practice questions on Direct and Inverse Proportions for, on Embibe.y

**Also, Check,**

**Attempt 8th CBSE Exam Mock Tests**

We hope that this Class 8 Math Chapter 13 article on NCERT Solutions Direct and Inverse Proportions Exercise 13.1 was helpful to you. For any further queries, drop us a comment below. Till then, stay tuned to **Embibe** for more updates on CBSE Chapter 13 Maths Class 8, exam tips and the latest academic articles!