Exercise 7.1 (Revised) - Chapter 8 - Comparing Quantities - Ncert Solutions class 8 - Maths

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NCERT Solutions for Class 8 Maths Chapter 7 - Comparing Quantities

Ex 7.1 Question 1.

Find the ratio of the following:
(a) Speed of a cycle $15 \mathrm{~km}$ per hour to the speed of scooter $30 \mathrm{~km}$ per hour.
(b) $5 \mathrm{~m}$ to $10 \mathrm{~km}$
(c) 50 paise to Rs. 5

Answer.

(a) Speed of cycle $=15 \mathrm{~km} / \mathrm{hr}$
Speed of scooter $=30 \mathrm{~km} / \mathrm{hr}$
Hence ratio of speed of cycle to that of scooter $=15: 30=\frac{15}{30}=\frac{1}{2}=1: 2$
(b) $\because 1 \mathrm{~km}=1000 \mathrm{~m}$
$\therefore 10 \mathrm{~km}=10 \times 1000=10000 \mathrm{~m}$
$\therefore$ Ratio $=\frac{5 \mathrm{~m}}{10000 \mathrm{~m}}=\frac{1}{2000}=1: 2000$
(c) $\because$ Rs $1=100$ paise
$\therefore$ Rs $5=5 \times 100=500$ paise
Hence Ratio $=\frac{50 \text { paise }}{500 \text { paise }}=\frac{1}{10}=1: 10$
Ex 7.1 Question 2.

Convert the following ratios to percentages:

(a) $3: 4$
(b) $2: 3$

Answer.

(a) Percentage of $3: 4=\frac{3}{4} \times 100 \%=75 \%$
(b) Percentage of $2: 3=\frac{2}{3} \times 100 \%=66 \frac{2}{3} \%$
Ex 7.1 Question 3.

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

Answer.

Total number of students $=25$
Number of good students in mathematics $=72 \%$ of $25=\frac{72}{100} \times 25=18$
Number of students not good in mathematics $=25-18=7$
Hence percentage of students not good in mathematics $=\frac{7}{25} \times 100=28 \%$
Ex 7.1 Question 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?

Answer.

Let total number of matches be $x$
According to question,

$
\begin{aligned}
& 40 \% \text { of total matches }=10 \\
& \Rightarrow 40 \% \text { of } x=10 \\
& \Rightarrow \frac{40}{100} \times x=10 \\
& \Rightarrow x=\frac{10 \times 100}{40}=25
\end{aligned}
$

Hence total number of matches are 25 .
Ex 7.1 Question 5.

If Chameli had Rs. 600 left after spending $75 \%$ of her money, how much money did

she have in the beginning?
Answer.

Total percentage of money she didn't spent $=100 \%-75 \%=25 \%$
According to question,
$
\begin{aligned}
& \Rightarrow 25 \%=600 \\
& \Rightarrow 1 \%=600 / 25 \\
& \Rightarrow 100 \%=\frac{600}{25} \times 100
\end{aligned}
$

Hence the money in the beginning was Rs 2,400.
Ex 7.1 Question 6.

If $60 \%$ people in a 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 are 50 lakh, find the exact number who like each type of game.

Answer.

Number of people who like cricket $=60 \%$
Number of people who like football $=30 \%$
Number of people who like other games $=100 \%-(60 \%+30 \%)=10 \%$
Now Number of people who like cricket $=60 \%$ of $50,00,000$

$
=\frac{60}{100} \times 50,00,000=30,00,000
$

And Number of people who like football
$
\begin{aligned}
& =30 \% \text { of } 50,00,000 \\
& =\frac{30}{100} \times 50,00,000=15,00,000 \\
& \therefore \text { Number of people who like other games }=10 \% \text { of } 50,00,000 \\
& =\frac{10}{100} \times 50,00,000=5,00,000
\end{aligned}
$

Hence, number of people who like other games are 5 lakh.