NCERT Solutions for Class 8 Maths Chapter 8: Comparing Quantities - Exercise 8.1

1. Find the Ratio of the Following:

(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.

Ans: The ratio of the speeds of cycle to scooter is given as \[R=\dfrac{15}{30}\].

Simplify \[R=\dfrac{15}{30}\] using division.

$R=\dfrac{15\div 15}{30\div 15}$

$=\dfrac{1}{2}$

Therefore, the ratio of speed of cycle 15 km per hour to speed of scooter 30 km per hour is $1:2$.

(b) 5 m to 10 km

Ans: 1 km can be written as 1000 m. Therefore 10 km is equal to 10000 m.

Ratio of 5 m to 10000 m is given as $R=\dfrac{5}{10000}$.

Simplify $R=\dfrac{5}{10000}$ using division.

$R=\dfrac{5\div 5}{10000\div 5}$

$=\dfrac{1}{2000}$

Therefore, the ratio of 5 m to 10 km is $1:2000$.

(c) 50 paise to Rs 5

Ans: Rs 1 can be written as 100 Paise. Therefore Rs 5 is equal to 500 Paise.

Ratio of 50 Paise to 500 rupees is given as $R=\dfrac{50}{500}$.

Simplify $R=\dfrac{50}{500}$ using division.

$R=\frac{50\div 50}{500\div 50}$

$=\frac{1}{10}$

Therefore, the ratio of 50 paise to Rs 5 is $1:10$.

2. Convert the following ratios to percentages:

(a) Convert ratio $3:4$ to percentage.

Ans: To convert ratio into percentage multiply the ratio by 100 and then add percentage sign to write the ratio as percentage.

Multiply ratio $3:4$ by 100 and add percentage sign and simplify.

$R=\dfrac{3}{4}\times 100\%$

$R =75\%$

Therefore, the ratio $3:4$ in percent can be written as $75\%$.

(b) Convert ratio $2:3$ to percentage.

Ans: To convert ratio into percentage multiply the ratio by 100 and then add percentage sign to write the ratio as percentage.

Multiply ratio $2:3$ by 100 and add percentage sign and simplify.

$R=\dfrac{2}{3}\times 100\%$ 

$R=\dfrac{200}{3}\%$ 

$R =66\frac{2}{3}\%$

Therefore, the ratio $2:3$ in percent can be written as $66\frac{2}{3}\%$.

3. $72\%$ of 25 students are good in Mathematics. How many are not good in Mathematics?

Ans: It is given that $72\%$ of 25 students are good at Mathematics.

Therefore, the percent of students who are not good at  Mathematics are $\left( 100-72 \right)\%=28\%$.

The number of students that aren’t good at Mathematics are $28\%$ of 25 students.

Thus, the number of students not good at Mathematics is $\dfrac{28}{100}\times 25$.

Simplify $\dfrac{28}{100}\times 25$ using division and multiplication.

$\Rightarrow \dfrac{28}{100}\times 25$ 

$\Rightarrow 7$

Thus, there are 7 students who are not good at Mathematics out of the total number of students.

4. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?

Ans: Let the total number of matches played by the football team be $x$.

It is given that the team won 10 matches and the winning percentage is $40% $. Thus, the expression can be written as $\dfrac{40}{100}\times x=10$.

Multiply both sides of the expression $\dfrac{40}{100}\times x=10$ by $\dfrac{100}{40}$ and simplify.

$\dfrac{40}{100}\times x\times \frac{100}{40}=10\times \frac{100}{40}$ 

$x=25$

Therefore, the team played a total of 25 matches.

5. If Chameli had Rs 600 left after spending $75\%$ of her money, how much did she have in the beginning?

Ans: Let the total amount of money that Chameli had in the beginning be $x$.

It is given that after spending $75\%$ of Rs$x$ she was left with Rs 600.

Thus, the expression can be written as $\left( 100-75 \right)\%\text{ of }x=600$.

Simplify expression $\left( 100-75 \right)\%\text{ of }x=600$ by converting percentage to fraction.

$\dfrac{25}{100}\times x=600$

Multiply both sides of the expression $\dfrac{25}{100}\times x=600$ by $\dfrac{100}{25}$ and simplify.

$\dfrac{25}{100}\times x\times \dfrac{100}{25}=600\times \dfrac{100}{25}$ 

$x=2400$

Therefore, she had Rs 2400 in the beginning.

6. If $60\%$ people in the city like cricket, $30\%$ like football and the remaining like other games, then what percent of the people like other games? If the total number of people is 50 lakh, find the exact number who like each type of game.

Ans: Percentage of people who like other games are $\left( 100-60-30 \right)\%$ that is $10%$.

It is given that the total number of people is 50 lakh.

Therefore, the number of people who like cricket is $60\%\text{ of }50$.

Simplify expression $60\%\text{ of }50$.

$\Rightarrow \frac{60}{100}\times 50$

$\Rightarrow 30$

Thus, 30 lakh people like cricket.

Therefore, the number of people who like football are $30\%\text{ of }50$.

Simplify expression $30\%\text{ of }50$.

$\dfrac{30}{100}\times 50=15$

Thus, 15 lakh people like football.

Therefore, the number of people who like games other than football and cricket are $10\%\text{ of }50$.

Simplify the expression $10\%\text{ of }50$.

$\dfrac{10}{100}\times 50= 5$

Thus, 5 lakh people like other games.

NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities (Ex 8.1) Exercise 8.1

Opting for the NCERT solutions for Ex 8.1 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 8.1 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 8 students who are thorough with all the concepts from the Subject Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 8 Maths Chapter 8 Exercise 8.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 8 Maths Chapter 8 Exercise 8.1, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

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