# NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities (EX 8.3) Exercise 8.3

The National Council of Educational Research and Training (NCERT), an official government entity, was founded to assist India’s schools in improving their educational standards. To establish a system of universal education, NCERT is in charge of creating and spreading the NCERT textbooks. It also produces instructional kits and multimedia digital assets to help students with their academics. Many Central Board of Secondary Education and state board schools employ NCERT textbook questions. The NCERT textbook includes various exercises. Students should carefully consider their answers to these exercise questions. These NCERT exercise problems provide the basis for the examinations’ final questions. Therefore, before the final examination, students should at the very least practise all of the exercise problems from the textbooks.

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“Comparing Quantities” refers to the units of two quantities that must match in order to be compared.. When two ratios are converted into like fractions, they can be compared. The two specified ratios are equivalent if the two fractions are equal. Students can use the NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3 to compute ratios and compare quantiles to find solutions to a variety of questions. Students will explore the concepts of ratio and proportion in the Class 7 Maths Chapter 8 Exercise 8.3 Solutions of the NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3. Additionally, they will learn about the unitary method, percentages, and simple interest concepts and how to use them in real-world situations. This chapter also discusses the conversion of fractions, decimals, and percentages into one another.

The Class 7 Maths Chapter 8 Exercise 8.3 is an important exercise of Class 7 Maths Chapter 8. Students must practise each topic appropriately if they want to achieve higher maths scores. By using the NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3, students can get better grades. Extramarks’ professionals provide step-by-step NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3 with clear and detailed explanations. Three exercises are included in the NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3. To help students improve their understanding of their essential concepts, so they can take on any difficulties connected to them, the NCERT textbook solutions are enough. Students should revise using sample papers and papers from previous years.Practice with the Class 7th Exercise 8.3 solutions can help students understand the concepts more thoroughly, leading to higher grades.Students frequently struggle to understand the NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3 because NCERT textbooks do not provide clear answers. Students may therefore find the comprehensive NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3 on the Extramarks website. Top educators with years of classroom experience have created the NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3. These experienced instructors have carefully prepared the notes and are aware of all the requirements. They are well-versed in the subject and are aware of the main points.They also comprehend the teacher’s psychology in great detail. Because of this, the vast majority of the examination questions are covered in this NCERT Solutions Class 7 Maths Chapter 8 Exercise 8.3.

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**NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities (EX 8.3) Exercise 8.3**

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

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**NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.3**

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**Q.1 **

$\begin{array}{l}\mathrm{Tell}\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{profit}\mathrm{or}\mathrm{loss}\mathrm{in}\mathrm{the}\mathrm{following}\mathrm{transactions}.\\ \mathrm{Also}\mathrm{find}\mathrm{profit}\mathrm{per}\mathrm{cent}\mathrm{or}\mathrm{loss}\mathrm{per}\mathrm{cent}\mathrm{in}\mathrm{each}\mathrm{case}.\\ \left(\mathrm{a}\right)\mathrm{Gardening}\mathrm{shears}\mathrm{bought}\mathrm{for}\u20b9250\mathrm{and}\mathrm{sold}\mathrm{for}\u20b9325.\\ \left(\mathrm{b}\right)\mathrm{A}\mathrm{refrigerater}\mathrm{bought}\mathrm{for}\u20b912,000\mathrm{and}\mathrm{sold}\mathrm{at}\u20b913,500.\\ \left(\mathrm{c}\right)\mathrm{A}\mathrm{cupboard}\mathrm{bought}\mathrm{for}\u20b92,500\mathrm{and}\mathrm{sold}\mathrm{at}\u20b93,000.\\ \left(\mathrm{d}\right)\mathrm{A}\mathrm{skirt}\mathrm{bought}\mathrm{for}\u20b9250\mathrm{and}\mathrm{sold}\mathrm{at}\u20b9150.\end{array}$

**Ans.**

\begin{array}{l}\text{(a) Cost price}=\text{\u20b9 250}\\ \text{Selling price}=\text{\u20b9 325}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Profit}=\text{\u20b9}\text{\hspace{0.17em}}\text{325}-\text{\u20b9}\text{\hspace{0.17em}}\text{250}\\ \text{}\text{}\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{}=\text{\u20b9}\text{\hspace{0.17em}}\text{75}\\ \text{}\text{Profit\%}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{\text{Profit}}{\text{Cost Price}}\times 100\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\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}}=\frac{75}{250}\times 100\\ \text{}\text{}\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}}=30\%\\ \text{(b) Cost price}=\text{\u20b9 12000}\\ \text{Selling price}=\text{\u20b9 13,500}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Profit}=\text{\u20b9}\text{\hspace{0.17em}}\text{13500}-\text{\u20b9}\text{\hspace{0.17em}}\text{1200}\\ \text{}\text{}\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{\u20b9}\text{\hspace{0.17em}}\text{1500}\\ \text{}\text{Profit\%}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{\text{Profit}}{\text{Cost Price}}\times 100\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\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}}=\frac{1500}{12000}\times 100\\ \text{}\text{}\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}}=12.5\%\\ \text{(c) Cost price}=\text{\u20b9 2500}\\ \text{Selling price}=\text{\u20b9 3,000}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Profit}=\text{\u20b9}\text{\hspace{0.17em}}\text{3000}-\text{\u20b9}\text{\hspace{0.17em}}\text{2500}\\ \text{}\text{}\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{\u20b9}\text{\hspace{0.17em}}\text{500}\\ \text{Profit\%}\text{}\text{}=\frac{\text{Profit}}{\text{Cost Price}}\times 100\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\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}}=\frac{500}{2500}\times 100\\ \text{}\text{}\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}}=20\%\\ \text{(d) Cost price}=\text{\u20b9 250}\\ \text{Selling price}=\text{\u20b9 150}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Loss}=\text{\u20b9}\text{\hspace{0.17em}}\text{250}-\text{\u20b9}\text{\hspace{0.17em}}1\text{50}\\ \text{}\text{}\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{\u20b9}\text{\hspace{0.17em}}\text{1000}\\ \text{}\text{Loss\%}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{\text{Loss}}{\text{Cost Price}}\times 100\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\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}}=\frac{100}{250}\times 100\\ \text{}\text{}\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}}=40\%\end{array}

**Q.2 **

$\begin{array}{l}\mathrm{Convert}\mathrm{each}\mathrm{part}\mathrm{of}\mathrm{the}\mathrm{ratio}\mathrm{to}\mathrm{percentage}:\\ \left(\mathrm{a}\right)3:1\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left(\mathrm{b}\right)2:3:5\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left(\mathrm{c}\right)1:4\; \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left(\mathrm{d}\right)\mathrm{1:\; 2:5.}\end{array}$

**Ans.**

\begin{array}{l}\left(\text{a}\right)\text{3}:\text{1}\\ \text{Here total parts}=3+1=4\\ {1}^{\text{st}}\text{part}=\frac{3}{4}=\frac{3}{4}\times 100\%=75\%\\ {2}^{\text{nd}}\text{part}=\frac{1}{4}=\frac{1}{4}\times 100\%=25\%\\ \left(\text{b}\right)\text{2}:\text{3}:\text{5}\\ \text{Here total parts}=2+3+5=10\\ {1}^{\text{st}}\text{part}=\frac{2}{10}=\frac{2}{10}\times 100\%=20\%\\ {2}^{\text{nd}}\text{part}=\frac{3}{10}=\frac{3}{10}\times 100\%=30\%\\ {3}^{\text{rd}}\text{part}=\frac{5}{10}=\frac{5}{10}\times 100\%=50\%\\ \left(\text{c}\right)\text{1}:\text{4}\\ \text{Here total parts}=1+4=5\\ {1}^{\text{st}}\text{part}=\frac{1}{5}=\frac{1}{5}\times 100\%=20\%\\ {2}^{\text{nd}}\text{part}=\frac{4}{5}=\frac{4}{5}\times 100\%=80\%\\ \left(\text{d}\right)\text{1}:\text{2}:\text{5}\\ \text{Here total parts}=1+2+5=8\\ {1}^{\text{st}}\text{part}=\frac{1}{8}=\frac{1}{8}\times 100\%=12.5\%\\ {2}^{\text{nd}}\text{part}=\frac{2}{8}=\frac{2}{8}\times 100\%=25\%\\ {3}^{\text{rd}}\text{part}=\frac{5}{8}=\frac{5}{8}\times 100\%=62.5\%\end{array}

**Q.3 **

$\begin{array}{l}\mathrm{The}\mathrm{population}\mathrm{of}\mathrm{a}\mathrm{city}\mathrm{decreased}\mathrm{from}25,000\mathrm{to}24,500.\\ \mathrm{Find}\mathrm{the}\mathrm{percentage}\mathrm{decrease}.\end{array}$

**Ans.**

\begin{array}{l}\text{Initial population}=2500\text{0}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Final populaton}=24500\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Decrease}=25000-2\text{4500}\\ \text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=500\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Decrease}\%=\frac{500}{25000}\times 100\\ =2\%\end{array}

**Q.4 **

$\begin{array}{l}\mathrm{Arun}\mathrm{bought}\mathrm{a}\mathrm{car}\mathrm{for}\u20b93,50,000.\mathrm{The}\mathrm{next}\mathrm{year},\mathrm{the}\mathrm{price}\\ \mathrm{went}\mathrm{up}\mathrm{to}\u20b93,70,000.\mathrm{What}\mathrm{was}\mathrm{the}\mathrm{Percentage}\mathrm{of}\mathrm{price}\\ \mathrm{increase}?\end{array}$

**Ans.**

\begin{array}{l}\text{Initial Price}=\text{\u20b9 3,50,000}\\ \text{Final Price}=\text{\u20b9 3,70,000}\\ \text{Increase}=\text{\u20b9}\text{\hspace{0.17em}}\text{3,70,000}-\text{\u20b9}\text{\hspace{0.17em}}\text{3,50,000}\\ \text{}\text{}\text{}=\text{\u20b9}\text{\hspace{0.17em}}\text{20,000}\\ \text{Increase\%}=\frac{20,000}{3,50,000}\times 100\\ \text{}=5\frac{5}{7}\%\end{array}

**Q.5 **

$\begin{array}{l}\mathrm{I}\mathrm{buy}\mathrm{a}\mathrm{T}.\mathrm{V}.\mathrm{for}\u20b9\mathrm{10,000}\mathrm{and}\mathrm{sell}\mathrm{it}\mathrm{at}\mathrm{a}\mathrm{profit}\mathrm{of}20\%.\mathrm{How}\\ \mathrm{much}\mathrm{money}\mathrm{do}\mathrm{I}\mathrm{get}\mathrm{for}\mathrm{it}?\end{array}$

**Ans.**

\begin{array}{l}\text{We know that}\\ \text{Profit\%}=\frac{\text{Profit}}{\text{Cost price}}\times 100\\ \text{So,}\\ \text{}20=\frac{\text{Profit}}{10,000}\times 100\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{\text{Profit}}{100\times \overline{)100}}\times \overline{)100}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Profit}=\text{20}\times \text{100}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\u20b9}\text{\hspace{0.17em}}\text{2000}\\ \text{Now,}\\ \text{}\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{Profit}=\text{Selling price}-\text{Cost price}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\u20b9}\text{\hspace{0.17em}}\text{2000}=\text{Selling price}-\text{\u20b9}\text{\hspace{0.17em}}\text{10000}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{Selling price}=\text{\u20b9}\text{\hspace{0.17em}}\text{10000}+\text{\u20b9}\text{\hspace{0.17em}}\text{2000}\\ \text{}\text{}\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{\u20b9}\text{\hspace{0.17em}}\text{12000}\end{array}

**Q.6 **

$\begin{array}{l}\mathrm{Juhi}\mathrm{sells}\mathrm{a}\mathrm{washing}\mathrm{machine}\mathrm{for}\u20b913,500.\mathrm{She}\mathrm{loses}20\%\mathrm{in}\\ \mathrm{the}\mathrm{bargain}.\mathrm{What}\mathrm{was}\mathrm{the}\mathrm{price}\mathrm{at}\mathrm{which}\mathrm{she}\mathrm{bought}\mathrm{it}?\end{array}$

**Ans.**

\begin{array}{l}\text{Selling price}=\text{\u20b9 135}00\\ \text{Loss}\%\text{}=\text{2}0\%\\ \text{Let the cost price be}x.\\ \therefore \text{Loss}=\text{2}0\%\text{of}x\\ \text{Cost price}-\text{Loss}=\text{Selling price}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{x}-20\%\text{of x}=\text{\u20b9}\text{\hspace{0.17em}}\text{13500}\\ \text{}\text{}\text{x}-\frac{20}{100}\times x=13500\\ \text{}\text{}\frac{100x-20x}{100}=13500\\ \text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{80x}{100}=13500\\ \text{}\text{}\text{}\text{}\text{\hspace{0.17em}}x=\frac{13500\times 100}{80}\\ \text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\u20b9}\text{\hspace{0.17em}}16875\end{array}

**Q.7 **

$\begin{array}{l}\left(\mathrm{i}\right)\mathrm{Chalk}\mathrm{contains}\mathrm{calcium},\mathrm{carbon}\mathrm{and}\mathrm{oxygen}\mathrm{in}\mathrm{the}\mathrm{ratio}\\ 10:3:12.\mathrm{Find}\mathrm{the}\mathrm{percentage}\mathrm{of}\mathrm{carbon}\mathrm{in}\mathrm{chalk}.\\ \left(\mathrm{ii}\right)\mathrm{If}\mathrm{in}\mathrm{a}\mathrm{stick}\mathrm{of}\mathrm{chalk},\mathrm{carbon}\mathrm{is}3\mathrm{g},\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{weight}\\ \mathrm{of}\mathrm{the}\mathrm{chalk}\mathrm{stick}.\end{array}$

**Ans.**

\begin{array}{l}\text{(i) Given ratio}=\text{10:3:12}\\ \text{}\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{Total}=\text{10}+\text{3}+\text{12}\\ =\text{25}\\ \text{Percentage of Carbon}=\frac{3}{25}\times 100\\ \text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=12\%\\ \text{(ii) Let the weight of the stick be x g}\\ \text{So, 12\% of x}=\text{3}\\ \text{}\frac{12}{100}\times x=3\\ \text{}\text{}x=\frac{300}{12}\\ \text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=25\text{\hspace{0.17em}}\text{g}\end{array}

**Q.8 **Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?

**Ans.**

\begin{array}{l}\text{Cost price of book}=\text{\u20b9 275}\\ \text{Loss\%}=\text{15}\\ \text{We have,}\\ \text{Loss\%}=\frac{\text{Loss}}{\text{Cost price}}\times 100\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}15=\frac{\text{Loss}}{275}\times 100\\ \text{}\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{Loss}=\frac{15\times 275}{100}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=41.25\\ \text{Selling price}=\text{Cost price}-\text{Loss}\\ \text{}\text{}\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{\u20b9}\text{\hspace{0.17em}}\text{275}-\text{\u20b9}\text{\hspace{0.17em}}\text{41}\text{.25}\\ \text{}\text{}\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{\u20b9 233}\text{.75}\end{array}

**Q.9** Find the amount to be paid at the end of 3 years in each case:

(a) Principal = ₹1,200 at 12% p.a.

(b) Principal = ₹7,500 at 5% p.a.

**Ans.**

\begin{array}{l}\text{(a)}\\ \text{\hspace{0.17em}}\text{Principal (P)}=\text{\u20b9 1200}\\ \text{}\text{Rate (R)}=\text{12\%}\\ \text{}\text{Time (T)}=3\text{years}\\ \text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{S}\text{.I}\text{.}=\frac{\text{P}\times \text{R}\times \text{T}}{100}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\text{}=\frac{1200\times 12\times 3}{100}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\text{}=\text{\u20b9}432\\ \text{}\text{Amount}=\text{P}+\text{S}\text{.I}\text{.}\\ \text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}=\text{\u20b9}\text{\hspace{0.17em}}\text{1200}+\text{\u20b9}\text{\hspace{0.17em}}\text{432}=\text{\u20b9 1632}\\ \text{(b)}\\ \text{Principal (P)}=\text{\u20b9 7500}\\ \text{}\text{Rate (R)}=\text{5\%}\\ \text{}\text{Time (T)}=\text{3 years}\\ \text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{S}\text{.I}\text{.}=\frac{\text{P}\times \text{R}\times \text{T}}{100}\\ \text{}\text{}\text{}=\frac{7500\times 5\times 3}{100}\\ \text{}\text{}\text{}=\text{\u20b9}1125\\ \text{}\text{Amount}=\text{P}+\text{S}\text{.I}\text{.}\\ \text{}\text{}\text{}=\text{\u20b9}\text{\hspace{0.17em}}\text{7500}+\text{\u20b9}\text{\hspace{0.17em}}\text{1125}\\ \text{}\text{}\text{}=\text{\u20b9 8625}\end{array}

**Q.10 **What rate gives ₹280 as interest on a sum of ₹56000 in 2 years?

**Ans.**

$\begin{array}{l}\mathrm{We}\mathrm{know}\mathrm{that}\\ \mathrm{S}.\mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100}\\ 280=\frac{\mathrm{56000}\times \mathrm{R}\times 2}{100}\\ \mathrm{R}=\frac{280\times 100}{56000\times 2}\\ =0.25\\ \mathrm{Therefore},\mathrm{the}\mathrm{rate}\mathrm{is}0.25\%.\end{array}$

**Q.11 **

$\begin{array}{l}\mathrm{If}\mathrm{Meena}\mathrm{gives}\mathrm{an}\mathrm{interest}\mathrm{of}\u20b945\mathrm{for}\mathrm{one}\mathrm{year}\mathrm{at}9\%\\ \mathrm{rate}\mathrm{p}.\mathrm{a}.\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{sum}\mathrm{she}\mathrm{has}\mathrm{borrowed}?\end{array}$

**Ans.**

\begin{array}{l}\text{We know that}\\ \text{S}\text{.I}=\frac{\text{P}\times \text{R}\times \text{T}}{100}\\ \text{So, we get}\\ \text{45=}\frac{\text{P\xd79\xd71}}{\text{100}}\\ \text{P=}\frac{\text{45\xd7100}}{\text{9}}\\ \text{=\u20b9}\text{\hspace{0.17em}}\text{500}\\ \text{Therefore, she borrowed \u20b9 500}\text{.}\end{array}