NCERT solutions class 8 maths chapter 8 comparing quantities is one of the most important study materials for the students studying in 8th standard. The comparing quantities solutions is prepared by expert mathematics teachers according to the latest syllabus and gudielines of the Central Board of Secondary Education.

The solutions provided here are extremely helpful for the students as they can clear their doubts instantly and understand the concepts in a better way. Also, check the NCERT class 8 maths chapter solutions pdfÂ provided at BYJU’S to access these solutions in offline mode.

### NCERT Solutions Class 8 Maths Chapter 8 Exercises

*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 lakh

Number 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

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 things easily, when the denominator are different. Thus students need to have a good practice of this chapter. In this chapter students will learn about the comparison of ratios, discounts, profit and loss condition on purchasing and selling of goods and many more. Along with these students will have a gist about the compound and simple interest on lending a certain amount depending upon the rate of interest and the time duration. All these concepts holds good in general life of everyone.

For students it is compulsory to have good understanding of these concepts, which will be useful to them in the life ahead. Students need to have a good practice of the various questions from the NCERT book. In order to excel examination, it is essential to have a good understanding of the topic, rather than just mugging the formulas and getting the solution.

Having a good practice of the NCERT questions will help students to have a good learning technique and good practice of all different types of questions that can be framed in the examination. 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 the solutions for comparing quantities, where they can get to know the different means of solving a question. Students can refer to difficult question of Maths NCERT in case of any doubt, or to clear their doubts, as we have covered all the basic concepts.