NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities

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Q.1: In a primary school, the parents were asked about the number of hours they spend per day in helping their children to do homework. There were 90 parents who helped for \(\frac{1}{2}\) hour to 1\(\frac{1}{2}\) hours. The distribution of parents according to the time for which, they said they helped is given in the adjoining figure ; 20% helped for more than 1\(\frac{1}{2}\) hours per day;
30% helped for 1 2 hour to 1\(\frac{1}{2}\) hours; 50% did not help at all. 
Using this, answer the following: 
(i) How many parents were surveyed?
(ii) How many said that they did not help? 
(iii) How many said that they helped for more than 1\(\frac{1}{2}\) hours?

Ans : Missing 

Q.2: Find the ratio of the following. 
(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. 
(b) 5 m to 10 km 
(c) 50 paise to  5

Ans : (a) Ratio of the speed of cycle to the speed of scooter \(=\frac{15}{30}=1 : 2\)
(b) Since 1 km = 1000 m, 
Required ratio = \(\frac{5 \mathrm{m}}{10 \mathrm{km}}=\frac{5 \mathrm{m}}{10 \times 1000 \mathrm{m}}=1 : 2000\)
(c) Since Re 1 = 100 paise, 
Required ratio = \(=\frac{50 \text { paise }}{\mathrm{Rs} 5}=\frac{50 \text { paise }}{500 \text { paise }}=1 : 10\) 

Q.3: Convert the following ratios to percentages.
(a) 3 : 4
(b) 2 : 3

Ans : \(\begin{array}{l}{3 : 4=\frac{3}{4}=\frac{3}{4} \times \frac{100}{100}=\frac{3}{4} \times 100 \%=75 \%} \\ {2 : 3=\frac{2}{3}=\frac{2}{3} \times \frac{100}{100}=\frac{2}{3} \times 100 \%=\frac{200}{3} \%} \\ {=\left(\frac{66 \times 3+2}{3}\right) \%=66 \frac{2}{3} \%}\end{array}\) 

Q.4: 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 good in mathematics. 
Percentage of students who are not good in mathematics = (100 — 72)% = 28% 
Therefore, Number Of students who are not good in mathematics = \(\frac{28}{100} \times 25\) = 7 
Thus, 7 students are not good in mathematics. 

Q.5: 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 team be x. 
It is given that the team won 10 matches and the winning percentage of the team was 40%. 
Therefore, 
\(\begin{array}{l}{\frac{40}{100} \times x=10} \\ {x=10 \times \frac{100}{40}} \\ {x=25}\end{array}\) 
Thus, the team played 25 matches. 

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