NCERT Solutions for Class 8 Maths Chapter 7 Comparing Quantities Ex 7.1

Exercise  7.1

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) $3:4$

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) $2:3$

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 interested in mathematics. How many are not interested in mathematics?

Ans: It is given that $72\%$ of 25 students are interested in mathematics.

Therefore, the percent of students who are not interested in mathematics are $\left( 100-72 \right)\%=28\%$.

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

Thus, the number of students not interested in 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 interested in 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.

Conclusion

NCERT Class 8 Chapter 7 Exercise 7.1, students learn about comparing quantities using ratios and percentages. This exercise helps students understand how to express one quantity as a fraction of another and convert it to a percentage. It's important to practice these concepts as they are used in everyday life, such as calculating discounts and comparing prices. By mastering these basics, students build a strong foundation for more advanced topics. Practice these problems to gain confidence and improve your math skills.

Class 8 Maths Chapter 7: Exercises Breakdown

CBSE Class 8 Maths Chapter 7 Other Study Materials

Chapter-Specific NCERT Solutions for Class 8 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

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