NCERT solutions class 8 maths chapter 8 comparing quantities is one of the most important study materials for the students to learn for the exam. The comparing quantities solutions are prepared by expert mathematics teachers according to the latest CBSE syllabus and guidelines.

The solutions provided here are extremely helpful for the students as they can clarify their doubts instantly and understand the concepts in a better way. Students can also practice exemplar problems and comparing quantities class 8 formulas provided here with us. Also, they should solve sample papers and previous year question paper to get an idea of questions asked from the chapter, comparing quantities and marking scheme for the same.

## Class 8 Maths NCERT Solutions for Comparing Quantities

In case of Natural numbers it is really easy to identify which is greater and which one is smaller, but when ratios and fractions are compared, it becomes very complex to differentiate them as the denominators are different. Thus students need to have a good practice of chapter 8, where students will learn about the comparison of ratios, discounts, profit and loss condition on purchasing and selling of goods and many more.

Class 8 NCERT solutions are provided for chapter 8 to download the PDF and also could be practised offline. These are helpful to score good marks in your main exams which are going to be conducted in 2019.

Here are the concepts of chapter 8:

- Brief introduction for Ratios & Percentages
- How to find Increase or Decrease Percent
- How to find Discounts
- Calculate cost price, selling price, profit % , loss%
- What are Sales Tax and Value Added Taxes
- Defining Simple Interest
- Defining Compound Interest
- About Compound Interest compounded half yearly
- Questions on Compound Interest for fraction years
- What are the Applications of Compound Interest Formula?

Along with these students will learn about the compound and simple interest in lending a certain amount depending upon the rate of interest and the time duration. These concepts are widely used in real-life scenarios.

### NCERT Solutions Class 8 Maths Chapter 8 Exercises

Read below to get exercise-wise solutions for chapter 8 of 8th class maths subject:

#### Comparing Quantities Class 8 Extra Questions

*Q1. Calculate Â the ratio for the following:*

*(i) The scooter runs with a speed of 30 km/hour and the cycle runs with a speed of 60 km/ hour.*

**Solution:**

Ratio of the speed of cycle to the speed of scooter = \(\frac{30}{60}\) = 1:2

(ii) 10 meter to 10 kilometer

Answer: Since 1 km = 1000 m

Required ratio = \(\frac{10\, m}{10\, km}\) = \(\frac{10\, m}{10 \times 1000\, m}\) = 1:1000

(iii) 30 paisa to Rs 3

Since Rs 1 = 100 paisa

Required ratio = \(\frac{30 \, paisa}{Rs\, 3}\) = \(\frac{30\, paisa}{300 \, paisa}\) = 1:10

*Q2. Change the given ratios into percentages.*

**Solution:**

(i) Â 4:5 = \(\frac{4}{5}\) = \(\frac{4}{5}\times\frac{100}{100}\)

= \(\frac{4}{5}\times 100\)% = 80%

(ii) 2:3=\(\frac{2}{3}\)= \(\frac{2}{3}\times \frac{100}{100}\)= \(\frac{2}{3}\times 100\)%= \(\frac{200}{3}\)%= \(\left ( \frac{66\times 3+2}{3} \right )\)%= \(66\frac{2}{3}\)%

*Q3. 72% of 25 students are doing well in maths. Find out how many students arenâ€™t doing well in maths.*

**Solution:**

Given , that 72% of 25 students are good in mathematics.

So, the percentage of students who are not doing well in mathematics=100%-72%=28%

\(âˆ´\)Number of students who are not good in mathematics = \(\frac{28}{100}\times 25\)=7 \(âˆ´\)7 students are not good in mathematics.

*Q4. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then calculate the number of matches they played in all.*

**Solution:**

Let the total number of matches played by the team be x.

Given, that the team won 10 matches and the winning percentage was 40%.

Therefore,

\(\frac{40}{100}\times x= 10\) \(x=10\times \frac{100}{40}\)X=25

\(âˆ´\)The team played 25 matches.

*Q5. If Charu had Rs 600 left after spending 75% of her money, how much did she have in the beginning?*

**Solution:**

Let the amount of money which Charu had in the beginning be x.

Given, that after spending 75% of Rs x, she was left with Rs 600.

Therefore,

(100 â€“ 75)% of x=Rs 600

So, 25% of x=Rs 600

\(\frac{25}{100}\times x=Rs\, 600\)X=Rs\(\left ( 600\times \frac{100}{25} \right )\)=Rs 2400

\(âˆ´\)She had Rs 2400 in the beginning.*Q6. If 30% like football 60% of Â people in a city like football, 60% like cricket and the rest like other games, then what percentage of the people like other games? If the total number of people are 50 lakh, find the exact number who like each type of game.*

**Solution:**

Percentage of people who like other games=100% – 60% – 30%

=(100-90)%

Total number of people in the city = 50 lakh

\(âˆ´\)Number of people who like cricket = \(\left ( \frac{60}{100}\times 50 \right )\) lakh=30 lakhNumber of people who like football=\(\left ( \frac{30}{100}\times 50 \right )\)lak =15 lakh

Number of people who like other games = \(\left ( \frac{10}{100}\times 50 \right )\) lakh = 5 lakh

**Bottom Line:**

Students need to have a good practice of the various questions from the exercises given in the NCERT book. In order to excel examination, it is essential to have a good understanding of the topic, rather than just by-hearting the formulas and getting the solution.

For the students of class 8, it is crucial to practice all the questions from the NCERT textbook to explore the different types of questions. BYJUâ€™S provide students with solutions for comparing quantities, where they can get to know the different methods or techniques of solving a question. Students can refer to these NCERT solutions for a quick revision at the time of final examination.

Students can download and try BYJUâ€™s â€“ The Learning app for a more interactive and seamless learning experience and to learn the concepts of Maths different topics with the help of videos.