# NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities (EX 8.2) Exercise 8.2

The Central Board of Secondary Education CBSE is one of India’s most prestigious and highly regarded educational boards.There are many schools that are affiliated with the CBSE board, and they are present everywhere in India. CBSE is a premier board when itcomes to imparting knowledge to students. CBSE has a very distinct curriculum and pattern that it asks its students to follow. The pattern is highly objective and the questions that are frequent in the exams are objective as well. An objective study pattern includes questions which are primarily short answer based. Such a curriculum demands that students go deep into the fundamental ideas that are being discussed in this chapter. Students must have a knack for new ideas and try to implement them in their lives. Students must have an in-depth understanding of the syllabus and its constituent chapters. CBSE designs its curriculum in a specific manner that facilitates students’ development of their analytical and cognitive abilities.. These traits in students are highly valued by the CBSE. Students cannot just memorise information from the chapter and get good grades. If students desire to get a good grade, then they must have a thorough understanding of the chapter.

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**NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities (EX 8.2) Exercise 8.2**

The NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.2 in Hindi and English provide the solutions for Chapter 8 of the Class 7 CBSE curriculum. In this chapter, students are taught how to understand and compare the different quantities.These are fundamental ideas that students must fully comprehend because the advanced ideas that will be covered in the student’s syllabus will be heavily reliant on them. Even these ideas will come back in other subjects like Physics, Chemistry, Economics etc. Therefore, the NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.2 in Hindi and English, helps students not only with Mathematics but with other subjects as well.

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**Access NCERT Solutions for Class 7 Maths Chapter 8 – Comparing Quantities**

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Click on the link below to access the Class 7 Maths Chapter 8 Exercise 8.2 Solutions.

**Q.1 **

$\begin{array}{l}\mathrm{Convert}\mathrm{the}\mathrm{given}\mathrm{fractional}\mathrm{numbers}\mathrm{to}\mathrm{per}\mathrm{cents}.\\ \left(\mathrm{a}\right)\frac{\mathrm{1}}{\mathrm{9}}\left(\mathrm{b}\right)\frac{\mathrm{5}}{\mathrm{4}}\left(\mathrm{c}\right)\frac{\mathrm{3}}{\mathrm{40}}\left(\mathrm{d}\right)\frac{\mathrm{2}}{\mathrm{7}}\end{array}$

**Ans.**

\begin{array}{l}\text{(a})\frac{1}{8}\\ =\frac{1}{8}\times \frac{100}{100}=\frac{1}{8}\times 100\%=12.5\%\\ \left(\text{b}\right)\frac{5}{4}\\ =\frac{5}{4}\times \frac{100}{100}=\frac{5}{4}\times 100\%=125\%\\ \left(\text{c}\right)\frac{3}{40}\\ =\frac{3}{40}\times \frac{100}{100}=\frac{3}{40}\times 100\%=7.5\%\\ \left(\text{d}\right)\frac{2}{7}\\ =\frac{2}{7}\times \frac{100}{100}=\frac{2}{7}\times 100\%=28\frac{4}{7}\%\end{array}

**Q.2** Convert the given decimal fractions to percents.

a. 0.65 b. 2.1 c. 0.02 d. 12.35

**Ans.**

\begin{array}{l}\left(\text{a}\right)\text{}0.\text{65}\\ =0.65\times 100\%=\frac{65\times 100}{100}\%=65\%\\ \left(\text{b}\right)\text{2}.\text{1}\\ =2.1\times 100\%=\frac{21\times 100}{10}\%=210\%\\ \left(\text{c}\right)\text{}0.0\text{2}\\ =0.02\times 100\%=\frac{2\times 100}{100}\%=2\%\\ \left(\text{d}\right)\text{12}.\text{35}\\ =12.35\times 100\%=\frac{1235\times 100}{100}\%=1235\%\end{array}

**Q.3** Estimate what part of the figures is coloured and hence find the percent which is coloured.

**Ans.**

\begin{array}{l}\text{(i)}\\ \text{From the figure, we observe that 1 part out of 4 is shaded,}\\ \text{so its}\frac{1}{4}.\\ \frac{1}{4}\times \frac{100}{100}=\frac{1}{4}\times 100\%=25\%\\ \text{(ii)}\\ \text{From the figure, we observe that 3 part out of 5 is shaded,}\\ \text{so its}\frac{3}{5}.\\ \frac{3}{5}\times \frac{100}{100}=\frac{3}{5}\times 100\%=60\%\\ \text{(iii)}\text{\hspace{0.17em}}\\ \text{From the figure, we observe that 3 part out of 8 is shaded,}\\ \text{so its}\frac{3}{8}.\\ \frac{3}{8}\times \frac{100}{100}=\frac{3}{8}\times 100\%=37.5\%\end{array}

**Q.4 **

$\begin{array}{l}\mathrm{Find}:\\ \left(\mathrm{a}\right)15\%\mathrm{of}250\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left(\mathrm{b}\right)1\%\mathrm{of}1\mathrm{hour}\\ \left(\mathrm{c}\right)20\%\mathrm{of}\mathrm{Rs}2500\; \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left(\mathrm{d}\right)75\%\mathrm{of}1\mathrm{k}\end{array}$

**Ans.**

\begin{array}{l}\left(\text{a}\right)\text{15}\%\text{of 25}0\\ =\frac{15}{100}\times 250=\frac{75}{2}=37.5\\ \left(\text{b}\right)\text{1}\%\text{of 1 hour}\\ \text{1 hour}=\text{60 minutes}\text{.}\\ \text{So, 1}\%\text{of 1 hour}\\ =\frac{1}{100}\times 60=\frac{6}{10}=\frac{3}{5}\\ \left(\text{c}\right)\text{2}0\%\text{of Rs 25}00\\ =\frac{20}{100}\times 2500=20\times 25=500\\ \left(\text{d}\right)\text{75}\%\text{of 1 kg}\\ \text{1 kg}=\text{1000 g}\text{.}\\ \text{So, 75}\%\text{of 1 kg}\\ =\frac{75}{100}\times 1000=75\times 10=750\end{array}

**Q.5 **

$\begin{array}{l}\mathrm{Find}\mathrm{the}\mathrm{whole}\mathrm{quantity}\mathrm{if}\\ \left(\mathrm{a}\right)5\%\mathrm{of}\mathrm{it}\mathrm{is}600.\left(\mathrm{b}\right)12\%\mathrm{of}\mathrm{it}\mathrm{is}\u20b91080.\\ \left(\mathrm{c}\right)40\%\mathrm{of}\mathrm{it}\mathrm{is}500\mathrm{km}.\left(\mathrm{d}\right)70\%\mathrm{of}\mathrm{it}\mathrm{is}14\mathrm{minutes}\\ 8\%\mathrm{of}\mathrm{it}\mathrm{is}40\mathrm{litre}\end{array}$

**Ans.**

\begin{array}{l}\left(\text{a}\right)\text{5}\%\text{of it is 6}00\text{is same as 5}\%\text{of x is 6}00.\\ \frac{5}{100}\times x=600\\ x=\frac{600\times 100}{5}=12000\\ \left(\text{b}\right)\text{12}\%\text{of it is}\u20b9\text{1}0\text{8}0\text{is same as 12}\%\text{of x is}\u20b9\text{\hspace{0.17em}}1080.\\ \frac{12}{100}\times x=1080\\ x=\frac{1080\times 100}{12}=\text{\hspace{0.17em}}\u20b9\text{\hspace{0.17em}}9000\\ \left(\text{c}\right)\text{4}0\%\text{of it is 5}00\text{km is same as 40}\%\text{of x is}500\text{\hspace{0.17em}}\text{km}.\\ \frac{40}{100}\times x=500\\ x=\frac{500\times 100}{40}=1250\\ \left(\text{d}\right)\text{7}0\%\text{of it is 14 minutes is same as 70}\%\text{of x is}14\text{\hspace{0.17em}}\text{minutes}\\ \frac{70}{100}\times x=14\\ x=\frac{14\times 100}{70}=20\\ \left(\text{e}\right)\text{8}\%\text{of it is 4}0\text{litres is same as 8}\%\text{of x is}40\text{\hspace{0.17em}}\text{litres}\\ \frac{8}{100}\times x=40\\ x=\frac{40\times 100}{8}=500\end{array}

**Q.6 **

$\begin{array}{l}\mathrm{Convert}\mathrm{given}\mathrm{per}\mathrm{cents}\mathrm{to}\mathrm{decimal}\mathrm{fractions}\mathrm{and}\mathrm{also}\mathrm{to}\\ \mathrm{fractions}\mathrm{in}\mathrm{simplest}\mathrm{forms}:\\ \left(\mathrm{a}\right)\mathrm{25\%}\left(\mathrm{b}\right)150\%\left(\mathrm{c}\right)\mathrm{20\%}\left(\mathrm{d}\right)\mathrm{5\%}\end{array}$

**Ans.**

\begin{array}{l}\left(\text{a}\right)\text{25}\%\\ =\frac{25}{100}=\frac{1}{4}=0.25\\ \left(\text{b}\right)\text{15}0\%\text{}\\ =\frac{150}{100}=\frac{15}{10}=\frac{3}{2}=1.5\\ \left(\text{c}\right)\text{2}0\%\\ =\frac{20}{100}=\frac{2}{10}=\frac{1}{5}=0.2\\ \left(\text{d}\right)\text{5}\%\\ =\frac{5}{100}=\frac{1}{20}=0.05\end{array}

**Q.7 **

$\begin{array}{l}\mathrm{In}\mathrm{a}\mathrm{city},\; 30\%\mathrm{are}\mathrm{females},\; 40\%\mathrm{are}\mathrm{males}\mathrm{and}\mathrm{remaining}\\ \mathrm{are}\mathrm{children}.\mathrm{What}\mathrm{percent}\mathrm{are}\mathrm{children}?\end{array}$

**Ans.**

\begin{array}{l}\text{Children}=\left(100-\left(30+40\right)\right)\%\\ =\left(100-70\right)\%\\ =30\%\end{array}

**Q.8 **

$\begin{array}{l}\mathrm{Out}\mathrm{of}15,000\mathrm{voters}\mathrm{in}\mathrm{a}\mathrm{constituency},\; 60\%\mathrm{voted}.\\ \mathrm{Find}\mathrm{the}\mathrm{percentage}\mathrm{of}\mathrm{voters}\mathrm{who}\mathrm{did}\mathrm{not}\mathrm{vote}.\mathrm{Can}\mathrm{you}\\ \mathrm{now}\mathrm{find}\mathrm{how}\mathrm{many}\mathrm{actually}\mathrm{did}\mathrm{not}\mathrm{vote}?\end{array}$

**Ans.**

\begin{array}{l}\text{Percentage of voters who voted}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=60\%\text{}\\ \text{Percentage of voters who did not vote}\text{\hspace{0.17em}}=\text{100\%-60\%}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{40\%}\\ \text{Number of voters who did not vote}=\text{40\% of 15,000}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{40}{100}\times 15000\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=6000\end{array}

**Q.9 **

$\begin{array}{l}\mathrm{Meeta}\mathrm{saves}\u20b9400\mathrm{from}\mathrm{her}\mathrm{salary}.\mathrm{If}\mathrm{this}\mathrm{is}10\%\mathrm{of}\mathrm{her}\\ \mathrm{salary}.\mathrm{What}\mathrm{is}\mathrm{her}\mathrm{salay}?\end{array}$

**Ans.**

\begin{array}{l}\text{Let her salary be x}\text{.}\\ \text{Then according to the question, we have}\\ \text{\hspace{0.17em}}\text{10\% of x}=\text{400}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{10}{100}\times x=400\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x=\frac{400\times 100}{10}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=4000\\ \text{Therefore Meeta\u2019s salary is \u20b9 4000}\end{array}

**Q.10 **

$\begin{array}{l}\mathrm{A}\mathrm{local}\mathrm{cricket}\mathrm{team}\mathrm{played}20\mathrm{matches}\mathrm{in}\mathrm{one}\mathrm{season}.\\ \mathrm{It}\mathrm{won}25\%\mathrm{of}\mathrm{them}.\mathrm{How}\mathrm{many}\mathrm{matches}\mathrm{did}\mathrm{they}\mathrm{win}?\end{array}$

**Ans.**

\begin{array}{l}\text{Since team played 20 matches,}\\ \text{So, number of matches won}=\text{25\% of 20}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{25}{100}\times 20\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{500}{100}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=5\\ \text{So, number they won 5 matchces}\end{array}