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April 11, 2024**NCERT Solutions for Comparing Quantities Exercise 8.1 Class 8 Maths: **The chapter lays primary focus on basic mathematical concepts for calculating and determining the value of money. As children we first learnt the numbers, their sequencing and then we were able to determine which number was small and which number was big. Now, the comparison is made in terms of percentages and fractions. This will further help in comparing quantities. The chapter explains the core concepts of comparison.

Maths Class 8 Chapter 8 Exercise 8.1 helps in performing the comparisons in a practical manner. There is a standard against which the quantities are compared. This lets us understand how much (more, less or equal) is one quantity when compared to another. We have provided detailed stepwise solutions here. All the solutions are prepared by experts at Embibe. We have provided the solutions in a PDF format and students can easily understand the problem solving methods.

Ex 8.1 Class 8 comprises a wide variety of questions that have been curated to understand and analyse the basic concepts of comparing the quantities. Students can practice many different variations and usages of them.

The topic of comparing the quantities is the fundamental for several high level Math concepts that the students may confront going ahead. Also, it is an essential skill needed to find solutions for practical real world problems. Practicing the problems is essential for developing Maths skills and this also helps the students in the exams. It especially helps students to save calculator time during the exams. Keep reading to find out the NCERT solutions for Maths Class 8 Chapter 8 Exercise 8.1.

Before knowing the solutions, let us first have a quick glance at all the topics of Comparing Quantities Exercise

Class 8 Maths Chapter 8 consists of the following topics.

S.No | Topic |

8.1 | Recalling Ratios and Percentages |

8.2 | Finding the Increase or Decrease Per cent |

8.3 | Finding Discounts |

8.3.1 | Estimation in percentages |

8.4 | Prices Related to Buying and Selling (Profit and Loss) |

8.4.1 | Finding cost price/selling price, profit %/loss% |

8.5 | Sales Tax/Value Added Tax |

8.6 | Compound Interest |

8.7 | Deducing a Formula for Compound Interest |

8.8 | Rate Compounded Annually or Half Yearly (Semi-Annually) |

8.9 | Applications of Compound Interest Formula |

Students can easily access the NCERT solutions for Maths Class 8 Chapter 8 Exercise 1 from below. Practising all the questions helps the students in getting well-versed with the concepts of comparing quantities exercise. Also, the confidence levels of the students increase as they attain perfection in the subject.

Comparing quantities is very much essential for people in their everyday lives. It revolves around the basics of mathematics. Considering the daily activities and scenarios that take place in our lives, comparisons play a key role and there is a need to explore different ways of comparing the quantities.

Students can access the PDF for Ex 8.1 Class 8 from below.

**Q.1: Calculate the amount and compound interest on ₹62,500 for 1 12 years at 8% per annum compounded half-yearly****Ans**: Given,

Principal amount (P) =₹ 62500

Rate of interest(R) = 8%

Time(T) = 112 years

There will be 3 half years in given 112 years.

i.e. 32years = 12×3 years = 3 half years

We know that, A=P1+R100n ⇒ A = ₹ 625001+41003 ⇒A = ₹ 62500×2625×2625×2625 ⇒ A = ₹ 70,304

Now, we know

Amount = Principle+ Compound interest

then, Compound interest = Amount in 3 half years-Principle amount

= ₹ 70304-62500

= ₹ 7,804.

Hence, the amount in 32 years is ₹ 70,304 and its compound interest is ₹ 7,804.

**Q.2: Calculate the amount and compound interest on ₹8,000 for 1 year at 9% per annum compounded half-yearly. (You could use the year by year calculation using SI formula to verify).****Ans**: Given,

Principal amount (P) = ₹ 8000

Rate of interest = 9%

Time =1 year

There are 2 half years in 1 year and rate would be 92% for each half year. We know that,

A=P1+R100n

⇒ A= 80001+92002 ⇒ A=80002092002 ⇒ A= ₹ 8736.20

Compound Interest =A-P

= ₹ (8736.20-8000)

= ₹ 736.20. Therefore, amount for 1 years is ₹ 8736.20 and compound interest

is ₹ 736.20

NCERT Solutions for Exercise 8.1 Class 8 Maths

The importance of knowing NCERT solutions for Class 8 Maths Exercise 8.1 is vast. It not only increases the chances of acquiring higher marks in the final exam, there are numerous benefits of solving NCERT solutions for Class 8 Maths Exercise 8.1. Let us explore some of the benefits here.

**Speedens Calculating Ability**

Quick calculating capabilities are very much required for the students to perform well and score good marks in the final exam. For some students, calculating the given Maths problem quickly comes easily while others struggle to calculate. However, everyone is capable of building this skill. The best way to improve your Maths skills is to practice the chapter-wise NCERT solutions everyday. This quickens the ability to deal with numbers, thereby enhancing the individual’s scope of performing well in the exam.

**Increases Scope of Higher Marks**

Students who practice the topic-wise NCERT solutions everyday can score maximum marks in the exam when compared to the students with minimal practice. As the students get well-versed with dealing with the problems while practising, it becomes easy for them to go ahead and derive the solution for the given problem with total confidence. To avoid feeling burdened during the last minute of exam, avoid the exam stress and to increase the scope of acquiring maximum marks, students are advised to practice the Maths Class 8 Chapter 8 Exercise 8.1 solutions.

**Builds Strong Fundamentals**

Strong fundamentals are necessary for the students to build a strong command over the subject. They are not only useful for scoring good marks in the exam but also help the students in several ways. Having strong basics of the subject is advantageous for students who wish to attempt the competitive exams. As most of the entrance exams these days have questions appearing from CBSE Maths subject of secondary and higher secondary education, it is important for the students to practice these questions beforehand.

Also, having strong basics helps students to easily grasp the complicated concepts that they may encounter during upper levels of education.

**Step by Step Explanation**

NCERT solutions explain the answers for given problems in a systematic way. Simplified steps are mentioned in the PDF. This enables the students to understand how exactly the solution has been derived. To perform a careful analysis of the solution and to be able to solve any problem of a similar kind, a stepwise explanation is very much important.

By understanding and solving each problem stepwise, students will be able to attain proficiency in problem solving.

**Exposure to Variety of Problems**

An exercise contains problems of different nature. A set of problems follows a certain method of problem solving approach. Students who practise all kinds of problems get exposed to a variety of problems and can solve any problem that comes their way. Instead of struggling to solve the question during exams or being stuck with the problem during exams, students can tackle any kind of problem with a smooth and hassle approach.

Therefore, to get familiar with all types of problems, it is important for the students to get exposed to a wide variety of problems and various methods to solve them.

Below-mentioned are some of the frequently asked questions related to Maths Class 8 Chapter 8 Exercise 8.1

**Q.1: What are the benefits of solving Class 8 Maths Chapter 8 Exercise 8.1?****Ans: **By solving all the problems of Exercise 8.1 Class 8 Maths, students can get exposed to different kinds of problems, understand the step-wise approach towards the problem, acquire strong basics of the subject, speeden their ability to calculate the problems quickly and increase the scope of acquiring good marks.

**Q.2: What does the Comparing Quantities Exercise teach the students?****Ans: **The topic of comparing quantities helps students in understanding and analysing the simple mathematical methods that are implemented for the comparison of quantities. Students can practice many different variations and usages of them.

**Q.3: Where can I find NCERT solutions for all problems of Class 8 Maths Exercise 8.1?****Ans: **Students can find detailed stepwise solutions for all the problems of Maths Class 8 Chapter 8 Exercise 8.1 at Embibe.

**Q4. What are the topics included in Comparing Quantities Exercise?****Ans: **Chapter 8 Comparing Quantities consists of topics such as Recalling Ratios and Percentages, Finding the Increase or Decrease Per cent, Finding Discounts, Estimation in percentages, Prices Related to Buying and Selling (Profit and Loss), Finding cost price/selling price, profit %/loss%, Sales Tax/Value Added Tax, Compound Interest, Deducing a Formula for Compound Interest, Rate Compounded Annually or Half Yearly (Semi-Annually) and Applications of Compound Interest Formula. Students can find detailed syllabus on CBSE official website

**Q.5: Calculate the amount and compound interest on ₹10,800 for 3 years at 1212% per annum compounded annually.****Ans: **Given,

Principal amount (P) = 10800

Time = 3 years

Rate = 252%

Thus, Amount is given by the formula: P1+R100n ⇒ A = ₹108001+252003

= ₹108002252003

=₹10800×225200×225200×225200

= ₹15377.34375

= ₹15377.34

Compound Interest =Amount in 3 years-Principal amount

=₹(15377.34-10800)

=₹4,577.34

Therefore, Compound Interest is ₹4,577.34

We hope this detailed article on the NCERT Solutions for Comparing Quantities Exercise 8.1 Class 8 Maths helps you. If you have any queries regarding this article on Exercise 8.1 Class 8 Maths, please ping us through the comment box below. We will get back to you as soon as possible.