# NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion (Ex 12.2) Exercise 12.2

Students often find Mathematics intimidating. Mathematical concepts, formulas, theorems, and calculations appear challenging to them. Due to the purely conceptual nature of this subject, students must be able to grasp its concepts at a deep level. Ratio and Proportion is the topics of Chapter 12 in Class 6. The concepts and calculations in this chapter might be difficult for students at first. With practise and guidance, the concepts and calculations will eventually become easier for them. Ratio and Proportion in Class 6 Mathematics Chapter-12 covers Introduction, Ratio, Proportion, and Unitary Method. Numerous exercises and questions are not included in the chapter, but various complex concepts are described. This may make it difficult for students to grasp these concepts and do well in the chapter. For students to perform effectively in their examinations, Extramarks provides them with all the essential resources to make their learning experience comprehensive and effortless.

NCERT textbooks do not include solutions to the exercises in the listed chapters. The Class 6 Math Exercise 12.2 provided by Extramarks helps students understand the questions given in the NCERT Textbooks while having a clear solution and approach to each question. In Mathematics, the NCERT textbook provides the foundation for all concepts. It is therefore important to practise  Class 6 Maths Chapter 12 Exercise 12.2. Students who have difficulty understanding these solutions may also use the learning modules provided by Extramarks. It provides students with the best educators, along with  Class 6 Maths Ch 12 Ex 12.2, so that they can easily understand these solutions and score well in the subject.

In India, CBSE is a national-level education board controlled by the government. The CBSE is affiliated with the majority of schools in the country. Founded in 1929, the board was a bold experiment in interstate cooperation and integration in secondary education. This board is followed by thousands of schools in India. Each year, CBSE conducts board examinations for Classes 10 and 12. NCERT is the curriculum used by CBSE-affiliated schools. In the NCERT curriculum, all the topics that can be asked in the examinations are covered. Therefore, Extramarks provides students with  Class 6 Maths Chapter 12 Exercise 12.2 Solutions.

Along with  Maths Class 6 Chapter 12 Exercise 12.2, Extramarks provides students with various learning modules so that students can learn comprehensively and perform effectively in their examinations. Extramarks is an organisation that proves the benefits of e-learning. With Extramarks’ K12 study materials, students can prepare for their examinations with complete and convenient materials. As a result of Extramarks’ detailed performance reports, students are able to self-assess and track their academic progress. During live doubt-solving classes, students have access to expert educators from Extramarks. As a result, they will be able to perform effectively in the examination by resolving their queries. Students can also go through the NCERT Class 6 Maths Chapter 12 Exercise 12.2 to resolve their doubts. Extramarks allows students to practise chapter-by-chapter worksheets, answer unlimited practise questions, take part in interactive activities, and more. Furthermore, the Learning App provides students with a visual learning journey to make learning easier and more enjoyable. In Extramarks, students learn through visuals and animations, so they do not find their studies boring. As a result of Extramarks, students have access to highly qualified and experienced educators who are experts in their fields.

## NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion (Ex 12.2) Exercise 12.2

Students can download the NCERT Maths Class 6 Chapter 12 Exercise 12.2 in PDF format. These solutions are easily accessible, and they can be downloaded and used offline, so students can review them whenever and wherever they want. The solutions to Class 6th Maths Chapter 12 Exercise 12.2 are curated by the expert educators of Extramarks and are properly detailed step by step. Before taking their exams, Extramarks recommends students review these solutions thoroughly. The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 helps students  understand the concept and logic behind every answer. In preparation for examinations, they are one of the best tools.

Going through the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 helps students with the basics of the chapter and also provides them with a steady calculation speed. Each of these solutions focuses on a specific area of the chapter. In addition to K12 Study Material for examinations, Extramarks offers Complete Syllabus Coverage, Media Rich Engaging Content, Curriculum Mapped Learning, and much more. Consequently, students are able to learn systematically and are not bored. Along with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, the website also provides them with the NCERT solutions for all the academic sessions and subjects. For NCERT Solutions Class 12, NCERT Solutions Class 11, NCERT Solutions Class 10, etc., students can refer to Extramarks. They can learn, practice, and clarify their doubts with the help of this website. Students should follow up with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 as they are designed by the subject experts of Extramarks and will ensure a smooth learning experience for all of them. Hence, if learners want to understand the concepts of the chapter, they should review Extramarks’ NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2.

The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 are easily available online. There are multiple portals that provide students with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. It is important for students to verify the credibility of the sources before using them. There are some learning platforms that are not credible. There are several platforms that offer the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, but only some of them work best for students. Extramarks is one of the best platforms for providing reliable study material to students. Apart from the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, it has multiple practise modules, past years’ papers, sample papers, and question banks for students. Using the platform, in-house experts from the industry bring together curriculum-based study material. Fact-checked and accurate information is provided to students. They can obtain an idea of the examination pattern by studying the sample papers and past years’ papers provided by Extramarks. Furthermore, they provide students with knowledge of the types of question that will appear in the examination, since the same kind of questions appears repeatedly. The answers in the examination should also be written in a specific way to achieve maximum marks. In addition, students should understand the marks distribution and topic weightage of the subject. A sample paper also provides students with a blueprint of the paper and a model for drafting their own. It is one of the best tools for them to revise quickly. Before taking the examinations, Extramarks recommends students review sample papers and past years’ papers.

## Access NCERT Solutions for Class 6 Maths Chapter 12- Ratio and Proportion

The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 provided by the Extramarks website, can be easily downloaded on any device. These solutions are explained in an easy language so that students can easily understand them. The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 are curated in very easy language so that students can understand them easily. When it comes to Mathematics, it’s all about critical thinking. Conceptual subjects enhance students’ problem-solving and analytical skills. Mathematics is undoubtedly a subject that requires extensive practice. Students must understand the basics of the subject in order to score well in it. Therefore, Extramarks provides them with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. Scientists believe that many scientific concepts are based on Mathematics. One NCERT textbook is included in the Class 6 Mathematics curriculum. Due to the extensive syllabus, students must work hard and have a solid understanding of each topic. For them to clear their basics, learning NCERT by heart is the first step. Mathematics Class 6 includes a chapter on Ratio and Proportion. There are many new concepts in this chapter that students may find challenging to comprehend. On the Extramarks website, students can find the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 which provide step-by-step explanations and detailed answers that greatly enhance their conceptual understanding. In accordance with the latest examination pattern, Extramarks’ subject experts have cross-checked and curated these answers. The Extramarks website provides students with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, which they can download and practise in order to achieve maximum marks in their examinations.

The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 are used by schools as the primary source for teaching students. They are a valuable resource for students who need clarification on their concepts. NCERT textbooks are heavily used in several schools since examinations are mostly based on NCERT fundamentals. The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 are therefore even more important for students to review carefully. Students in classes 11 and 12 often use these solutions to prepare for board examinations. Through the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, they will be able to practise and clarify the concepts, so they are able to solve any complicated problem during the examination. However, students of Class 6 should practise a number of questions before sitting for the examinations, not just the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. To gain a deeper understanding of concepts, it is essential to practice the NCERT textbook questions thoroughly. Extramarks offers students a variety of learning tools, such as K12 study materials, to help them excel in their studies. The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2  is an example of one such learning tool where students can understand and learn about the concepts and achieve success in their examinations.

## NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2

It is important for students to have a comprehensive study guide so that their learning process can be easy and systematic. Extramarks provides them with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 which are properly organised answers to Chapter 12 Class 6. As these solutions are provided by the best educators, students can easily understand the chapter. The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 also save students’ time as they do not have to find these solutions elsewhere. Additionally, they can use it to maintain a comprehensive index of their curriculum and revisions. Students in Class 6 should recall the topics they have already studied. Therefore, Extramarks provides them with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 and all the means necessary to obtain high scores in the examinations. Easy-to-access and well-explained step-by-step solutions are provided here. The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 provided by Extramarks are the most straightforward answers that students can find on the internet. By practising these solutions, they gain a better understanding of the chapter’s concepts, thereby increasing their academic efficiency.

Learning new concepts can be challenging for students. It is common for them to have doubts and problems when learning these new concepts. In mathematics, every concept in each chapter must be understood because it is a purely conceptual subject. A lot of properties, operations, and concepts are introduced in every exercise in every chapter. Keeping track of all these concepts can be difficult for students. Therefore, Extramarks provides students with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 for a deeper and better understanding of the concepts of the chapter. Furthermore, Extramarks offers them learning modules such as K12 study material, live doubt-solving sessions, and assessment centres. This allows students to keep track of all the topics they have already covered, as well as the ones they need to practice more. Thus, they can achieve their goals and achieve good results in their examinations. NCERT Textbooks do not contain solutions, so students have difficulty finding accurate and detailed answers to questions. There is no doubt that it can be very tiresome to find the answers on various portals, and it can be time-consuming as well. The Extramarks website provides students with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, along with the solutions to a variety of other chapters. Through these solutions, they can find authentic solutions without wasting valuable time searching for them.

Students need detailed and step-by-step solutions, as well as a number of questions and question banks to practise before the examination. The majority of the question banks are based on NCERT textbooks. Students can prepare better for their examinations by using the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 available on the Extramarks website. In order to feel confident about their examinations, students must have good learning methods.Students can move forward with their preparation by understanding the concepts of the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. It can be difficult to understand the concepts in this chapter at times, but Extramarks’ NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 can be a beneficial resource. Using these learning modules can make practising Mathematics easier and more enjoyable.

The NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 provided by Extramarks can be accessed online and offline, thus making it convenient for students to revise anywhere and anytime. It may be confusing at times to follow the steps and formulas in the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. Students should pay attention to the steps and calculations involved. There might be some portals that are unreliable for accessing these solutions. There are some complex and confusing concepts and functions in this chapter. A credible source of the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 can facilitate the process of learning and preparation for the examination. These solutions are reliable since they are compiled by academic experts. The solutions are based on the answers provided in the NCERT textbooks and follow the same steps. In order to access the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, students can visit the Extramarks website. Additionally, the website offers extensive study material to help students clarify concepts before examinations. Students who have difficulty understanding this chapter can use the study material available on Extramarks. Furthermore, along with practising the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 students can go through the entire exercises for each unit and chapter. It may help them to ensure they do not miss anything crucial for their examinations or for understanding the concepts covered in the chapter.

Q.1 Determine if the following are in proportion.
(a) 15, 45, 40, 120 (b) 33, 121, 9,96
(c) 24, 28, 36, 48 (d) 32, 48, 70, 210
(e) 4, 6, 8, 12 (f) 33, 44, 75, 100

Ans.

(a) Ratio of 15 and 45 = 15:45
= 1:3
Ratio of 40 and 120 = 40:120
= 1:3
Since, 15:45 = 40:120
Therefore, 15, 45, 40 and 120 are in proportion.

(b) Ratio of 33 and 121= 33:121
= 3:11
Ratio of 9 and 96 = 9:96
= 3:32
since, 33:121 ≠ 9:96
Therefore, 33, 121, 9 and 96 are not in proportion.
(c) Ratio of 24 and 28 = 24:28
= 6:7
Ratio of 36 and 48 = 36:48
= 3:4
since, 24:28 ≠ 36:48
Therefore, 24, 28, 36 and 48 are not in proportion.

(d) Ratio of 32 and 48 = 32:48
= 2:3
Ratio of 70 and 210 = 70:210
= 1:3
since, 32:48 ≠ 70:210
Therefore, 32, 48, 70 and 210 are not in proportion.
(e) Ratio of 4 and 6 = 4:6
= 2:3
Ratio of 8 and 12 = 8:12
= 2:3
since, 4:6 = 8:12
Therefore, 4, 6, 8 and 12 are in proportion.
(f) Ratio of 33 and 44 = 33:44
= 3:4
Ratio of 75 and 100 = 75:100
= 3:4
since, 33:44 = 75:100
Therefore, 33, 44, 75 and 100 are in proportion.

Q.2 Write True (T) or False (F) against each of the following statements:
(a) 16 : 24 :: 20 : 30 (b) 21: 6 :: 35 : 10
(c) 12 : 18 :: 28 : 12 (d) 8 : 9 :: 24 : 27
(e) 5.2 : 3.9 :: 3 : 4 (f) 0.9 : 0.36 :: 10 : 4

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 16 and 24}=\frac{16}{24}\\ =\frac{8×2}{8×3}\\ =\frac{2}{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 20 and 30}=\frac{20}{30}\\ =\frac{10×2}{10×3}\\ =\frac{2}{3}\\ \mathrm{So},\text{â€‹ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}16:24::20:30}\\ \mathrm{Therefore},\text{it is true.}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 21 and 6}=\frac{21}{6}\\ =\frac{3×7}{3×2}\\ =\frac{7}{2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 35 and 10}=\frac{35}{10}\\ =\frac{5×7}{5×2}\\ =\frac{7}{2}\\ \mathrm{So},\text{â€‹ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}21:6::35:10}\\ \mathrm{Therefore},\text{it is true.}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 12 and 18}=\frac{12}{18}\\ =\frac{6×2}{6×3}\\ =\frac{2}{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 28 and 12}=\frac{28}{12}\\ =\frac{4×7}{4×3}\\ =\frac{7}{3}\\ \mathrm{So},\text{â€‹ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}12:18}\ne \text{28:12}\\ \mathrm{Therefore},\text{it is False.}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 8 and 9}=\frac{8}{9}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 24 and 27}=\frac{24}{27}\\ =\frac{3×8}{3×9}\\ =\frac{8}{9}\\ \mathrm{So},\text{â€‹ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}8:9}=\text{24:27}\\ \mathrm{Therefore},\text{it is True.}\\ \left(\mathrm{e}\right)\text{\hspace{0.17em}}\mathrm{Ratio}\text{of 5.2 and 3.9}=\frac{5.2}{3.9}\\ =\frac{1.3×4}{1.3×3}\\ =\frac{4}{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 3 and 4}=\frac{3}{4}\\ \mathrm{So},\text{â€‹ \hspace{0.17em}\hspace{0.17em}5.2:3.9}\ne \text{3:4}\\ \mathrm{Therefore},\text{it is False.}\\ \left(\mathrm{f}\right)\text{\hspace{0.17em}}\mathrm{Ratio}\text{of 0.9 and 0.36}=\frac{0.9}{0.36}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{0.9×1}{0.9×4}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{1}{4}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of 10 and 4}=\frac{10}{4}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{2×5}{2×2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{5}{2}\\ \mathrm{So},\text{â€‹ \hspace{0.17em}0.9:0.36}\ne \text{10:4}\\ \mathrm{Therefore},\text{it is False.}\end{array}$

Q.3 Are the following statements true?
(a) 40 persons: 200 persons = 15: 75
(b) 7.5 litres: 15 litres = 5 kg: 10 kg
(c) 99 kg: 45 kg = 44: 20
(d) 32 m: 64 m = 6 sec: 12 sec
(e) 45 km: 60 km = 12 hours: 15 hours

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\text{Ratio of 40 persons and 200 persons}=\frac{40}{200}\\ =\frac{40×1}{40×5}\\ =\frac{1}{5}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 15 and 75}=\frac{15}{75}\\ =\frac{15×1}{15×5}\\ =\frac{1}{5}\\ \mathrm{So},\text{}40\text{}\mathrm{persons}:200\text{}\mathrm{persons}=\text{}15:\text{}75\\ \mathrm{Therefore},\text{the given statement is true.}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 7.5 litres and 15 litres}=\frac{7.5}{15}\\ =\frac{7.5×1}{7.5×2}\\ =\frac{1}{2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 5 kg and 10 kg}=\frac{5}{10}\\ =\frac{5×1}{5×2}\\ =\frac{1}{2}\\ \mathrm{So},\text{}7.5\text{}\mathrm{litres}:15\text{}\mathrm{litres}=5\text{}\mathrm{kg}:10\text{\hspace{0.17em}}\mathrm{kg}.\\ \mathrm{Therefore},\text{the given statement is true.}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 99 kg and 45 kg}=\frac{99}{45}\\ =\frac{9×11}{9×5}\\ =\frac{11}{5}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 44 and 20}=\frac{44}{20}\\ =\frac{4×11}{4×5}\\ =\frac{11}{5}\\ \therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}99\text{}\mathrm{kg}:45\text{}\mathrm{kg}=\text{}44:\text{}20.\\ \mathrm{Therefore},\text{the given statement is true.}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 32 m and 64 m}=\frac{32}{64}\\ =\frac{32×1}{32×2}\\ =\frac{1}{2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 6\hspace{0.17em}sec and 12\hspace{0.17em}sec}=\frac{6}{12}\\ =\frac{6×1}{6×2}\\ =\frac{1}{2}\\ \therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}32\text{}\mathrm{m}:64\text{}\mathrm{m}=6\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{sec}:12\text{\hspace{0.17em}}\mathrm{sec}.\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Therefore},\text{the given statement is true.}\\ \left(\mathrm{e}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 45 km and 60 km}=\frac{45}{60}\\ =\frac{3×15}{4×15}\\ =\frac{3}{4}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of 12 hours and 15 hours}=\frac{12}{15}\\ =\frac{3×4}{3×5}\\ =\frac{4}{5}\\ \therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}45 km}:\text{60 km}\ne \text{12 hours}:\text{15 hours}.\\ \mathrm{Therefore},\text{the given statement is false.}\end{array}$

Q.4 Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm : 1 m and 40 : 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
(c) 2 kg: 80 kg and 25 g: 625 g
(d) 200 ml : 2.5 litre and 4 : 50

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of}25\text{}\mathrm{cm}\text{and}1\text{}\mathrm{m}=\frac{25}{100}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{1}{4}\\ \text{\hspace{0.17em}\hspace{0.17em}}\mathrm{Ratio}\text{of}\text{}40\text{and}\text{}160=\frac{40}{160}\\ =\frac{40×1}{40×4}\\ =\frac{1}{4}\\ \mathrm{Here},\text{\hspace{0.17em}}25\text{}\mathrm{cm}:1\text{}\mathrm{m}=\text{}40:\text{}160.\\ \mathrm{So},\text{}25\text{}\mathrm{cm}:1\text{}\mathrm{m}\text{}\mathrm{and}\text{}\text{}40:\text{}160\text{are in proportion.}\\ \text{Middle terms of the proportion are: 1m and 40.}\\ \text{Extreme terms of the proportion are: 25 cm and 160.}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}Ratio of}39\text{}\mathrm{litres}\text{}\mathrm{and}\text{}65\text{}\mathrm{litres}=\frac{39}{65}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{13×3}{13×5}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{3}{5}\\ \text{\hspace{0.17em}\hspace{0.17em}Ratio}\mathrm{of}\text{\hspace{0.17em}}6\text{}\mathrm{bottles}\text{}\mathrm{and}\text{}10\text{}\mathrm{bottles}=\frac{6}{10}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{2×3}{5×5}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{3}{5}\\ \mathrm{Here},\text{\hspace{0.17em}}39\text{}\mathrm{litres}:65\text{}\mathrm{litres}=6\text{}\mathrm{bottles}:10\text{}\mathrm{bottles}.\\ \mathrm{So},\text{}39\text{}\mathrm{litres}:65\text{}\mathrm{litres}::6\text{}\mathrm{bottles}:10\text{}\mathrm{bottles}\text{are in proportion.}\\ \text{Middle terms of the proportion are:}65\text{}\mathrm{litres}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}\hspace{0.17em}}6\text{}\mathrm{bottles}\text{.}\\ \text{Extreme terms of the proportion are:}39\text{}\mathrm{litres}\text{and}10\text{}\mathrm{bottles}\text{.}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of}2\text{}\mathrm{kg}\text{}\mathrm{and}\text{}80\text{}\mathrm{kg}=\frac{2}{80}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{1}{40}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio}\mathrm{of}\text{\hspace{0.17em}}25\text{}\mathrm{g}\text{}\mathrm{and}\text{}625\text{}\mathrm{g}=\frac{25}{625}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{25×1}{25×25}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{1}{25}\\ \mathrm{Here},\text{\hspace{0.17em}}2\text{}\mathrm{kg}:80\text{}\mathrm{kg}\ne 25\text{}\mathrm{g}:625\text{}\mathrm{g}.\\ \mathrm{So},\text{}2\text{}\mathrm{kg}:80\text{}\mathrm{kg}\text{}\mathrm{and}\text{\hspace{0.17em}}25\text{}\mathrm{g}:625\text{}\mathrm{g}\text{are}\mathrm{not}\text{in proportion.}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio of}200\text{}\mathrm{ml}\text{}\mathrm{and}\text{}2.5\text{}\mathrm{l}=\frac{200}{2500}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left[âˆµ1\mathrm{l}=1000\text{\hspace{0.17em}}\mathrm{ml}\right]\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{2}{25}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Ratio}\mathrm{of}\text{\hspace{0.17em}}4\text{}\mathrm{and}\text{}50=\frac{4}{50}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{2×2}{2×25}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{2}{25}\\ \mathrm{Here},\text{\hspace{0.17em}}200\text{}\mathrm{ml}:2.5\text{}\mathrm{l}::4:50.\\ \mathrm{So},\text{}200\text{}\mathrm{ml}:2.5\text{}\mathrm{l}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}\hspace{0.17em}}4:50\text{are in proportion.}\\ \text{Middle terms of the proportion are: 2.5}\mathrm{litres}\text{and}4.\\ \text{Extreme terms of the proportion are: 200 ml and 50.}\end{array}$

## 1. Where can students find the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2?

Yes, the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 are available on the Extramarks website. To assist students with complicated problems, Extramarks provides detailed solutions that are presented in a step-by-step manner. Students can easily access the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 both online and offline as they can be downloaded in PDF format. It is possible for them to revise these solutions at any time and anywhere. Along with the NCERT Solutions Class 6 Maths Chapter 12 Exercise Furthermore, Extramarks provides students with learning modules such as complete syllabus coverage, K12 study materials, in-depth performance reports, live classes from top faculty, and doubt-solving sessions. As a result, students may be able to perform better in their examinations.

## 2. How can students prepare for the Class 6 Mathematics examinations?

It is important to practice Mathematics rigorously. NCERT curriculum should be the first and foremost step for students in preparing for their examinations. Therefore, Extramarks recommends students thoroughly go through the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. They should also go through the Important questions, revision notes, sample papers, and past years’ papers. By using these tools and the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2, students are able to record their preparation level as well as get a sense of the types of questions they may face in the examination. These tools also provide students with information about the subject’s marking scheme and chapter weightage. As a result of these tools, they are able to perform well in their examinations. Students are able to determine their preparation level as well as their strengths and weaknesses in the curriculum by practising the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. They can use these tools to quickly review the chapter since they highlight the key points. The past years’ papers and sample papers of the subject’s curriculum should be reviewed carefully by students. Developing strong concepts of the subject allows them to solve any complicated problem that may arise during their examinations. Also, sample papers and past years’ papers aid students in preparing for their examinations, so they can avoid any last-minute challenges and perform well.

## 3. Is it important to practice all the questions of the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2?

Yes, students should practice all the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 as every question introduces them to new concepts and improves their mathematical skills of students. Additionally, Mathematics is a subject that requires ample practice for them to succeed. For this reason, it is essential for students to practice a number of questions in order to become efficient in Mathematics. Extramarks recommends them to thoroughly review the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 prior to their examinations. Class 6 Mathematics examinations are also based on the NCERT curriculum. NCERT questions can therefore appear in the examinations. Furthermore, the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 also help in strengthening the fundamentals of students so that they can solve any complicated question that can appear in the examinations. Mathematics contains a variety of concepts and calculations that can be challenging for students, so practice is essential. Additionally, students should become used to learning comprehensively from their smaller academic sessions. Therefore, they should be thorough with the concepts of the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2.

## 4. How many chapters are there in the curriculum of Class 6 Mathematics?

There are fourteen chapters in the NCERT textbook of Class 6 Mathematics. Extramarks provides students with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 and many other learning tools which provide them with a comprehensive and enjoyable learning process. It is also recommended that students practice the NCERT Exemplar questions in order to score well in any in-school or competitive examination. Through Extramarks, they can have access to a variety of tools and resources to help them learn, practice, and excel in their studies.

## 5. Are the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 difficult?

No, the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 are not difficult, however, they help students to have a better understanding of the curriculum of the chapter. Furthermore, the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2  are also incorporated in a very easy-to-understand language so that they do not face any issue in grasping the concepts of the chapter. Practising them also helps students resolve their doubts and avoid small calculation mistakes. It can sometimes be challenging for students to grasp the facts and concepts of Chapter 12 Class 6 Mathematics. In spite of this, they can master all the chapters of Class 6 Mathematics with proper guidance and regular practice. In Class 6, Mathematics is one of the most scoring subjects. Extramarks recommends students to thoroughly review the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 prior to their examinations.

## 6. What are the benefits of practising the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2?

There are numerous benefits of reviewing the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. These solutions outline the basic concepts of the chapter, so it is important for students to understand them. Also, the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 make it easier for the students to understand the concepts of the chapter as they are curated by Extramarks subject experts. As a result, students are able to grasp the concepts without having to deal with any linguistic difficulties. The Extramarks website provides students with all the resources they need to succeed in examinations and grow academically. Since these solutions are curated in a clear and simple manner, students can easily understand the concepts of the chapter. Furthermore, these solutions also provide learners with an idea of the format in which answers should be written in the examinations. Since the subject’s curriculum is entirely based on the NCERT curriculum, these solutions are also used as the primary source of teaching in CBSE schools.

## 7. Why should students choose Extramarks as their learning partner?

Extramarks is a platform that has taken an initiative to provide students with all the means necessary for their examinations like the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. The platform is available worldwide. Using its trustworthy, complete, and up-to-date study material, students can score maximum marks in any examination. Also, the learning website makes sure that they complete all their syllabus on time and do not leave any essential topics, including the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. Extramarks’ learning tools enable students to learn effectively and efficiently. The Extramarks website offers a variety of tools, including In-Depth Performance Reports. Chapter-by-chapter worksheets are provided with the Learn Practice Tests to assist them in tracking their academic progress. Students can learn at their own pace with Extramarks. The website also provides students with Complete Syllabus Coverage, which helps students to cover their entire curriculum along with the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 on time without feeling burdened. Gamified Learning Experience is also offered by Extramarks

so that their studies are not monotonous. There are several other learning modules available on the Extramarks website, including the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. Students can improve their academic performance by subscribing to the Extramarks website.

## 8. How can students clear their doubts related to the Class 6 Mathematics Chapter 12 Ratio and Proportion?

Students’ academic performance has always been a priority goal of the Extramarks website. Extramarks provides them with all the resources they need to learn, practice, and excel in their studies like the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2. Students can clear their doubts about the subject’s curriculum through Live Doubt Solving Classes and K12 Live Classes, and much more. These modules help students to interact live with their teachers and resolve all their doubts in order to have a solid foundation in the subject. A recording of these lectures can also be used for further assistance. Students can manage all their classes and subjects comprehensively with the assistance of Extramarks. Having a bright academic future is possible for students by subscribing right away to the Extramarks website.

## 9. Are the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 provided by Extramarks reliable?

Yes, the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 provided by Extramarks are credible sources for the preparation of examinations. Expert educators at Extramarks examine and cross-check these solutions. Keeping up with the latest examination patterns, the solutions, are the best resource for preparing for examinations. Moreover, the NCERT Solutions Class 6 Maths Chapter 12 Exercise 12.2 are also helpful for the preparation of various other competitive examinations. A step-by-step approach and straightforward language are used to curate these solutions. As a result, students should be very thorough when they are solving these solutions. Since these solutions are compiled by highly qualified and experienced teachers, these solutions are very comprehensive and trustworthy. Furthermore, these solutions are also helpful in developing the problem-solving and analytical skills of students and therefore, they are one of the best tools for the preparation of the students.