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# NCERT Solutions for Class 8 Maths Chapter 7 Comparing Quantities

Last updated date: 20th Sep 2024
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## Complete Resource of NCERT Solutions Maths Chapter 7 Class 8 - Free PDF Download

Class 8 Maths NCERT Solutions for Chapter 7 Comparing Quantities is an important topic that introduces students to various concepts such as ratios, percentages, and their applications in real-life situations. This chapter helps students understand how to compare different quantities using mathematical expressions and formulas.

Table of Content
1. Complete Resource of NCERT Solutions Maths Chapter 7 Class 8 - Free PDF Download
2. Glance on Maths Chapter 7 Class 8 - Comparing Quantities
3. Access Exercise wise NCERT Solutions for Chapter 7 Maths Class 8
4. Exercises Under NCERT Solutions for Class 8 Maths Chapter 7 Comparing Quantities
4.1Exercise 7.1:
4.2Exercise 7.2:
4.3Exercise 7.3:
5. Access NCERT Solutions for Class 8 Maths Chapter 7 – Comparing Quantities
5.1Exercise: 7.1
5.2Exercise 7.2
5.3Exercise 7.3
6. Overview of Deleted Syllabus for CBSE Class 8 Comparing Quantities Maths Chapter 7
7. Class 8 Maths Chapter 7: Exercises Breakdown
8. Other Study Material for CBSE Class 8 Maths Chapter 7
9. Chapter-Specific NCERT Solutions for Class 8 Maths
FAQs

Students should focus on key areas like calculating simple and compound interest, understanding profit and loss, and determining discounts and taxes. The chapter is designed to build a strong foundation in these concepts, which are important for solving practical problems.  Access the latest CBSE Class 8 Maths Syllabus here.

## Glance on Maths Chapter 7 Class 8 - Comparing Quantities

• Formulas included in this chapter are calculating percentages, profit and loss percentages, compound interest, and simple interest.

• The chapter contains solved examples, practice problems, and exercises involving direct calculation, real-life application, and conceptual questions.

• This offers a varied range of questions to enhance understanding and application of concepts.

• These chapter exercises are designed to reinforce mathematical concepts related to everyday calculations, financial literacy, and effective problem-solving skills in real-world contexts.

• There are three exercises (14 fully solved questions) in Chapter 7 Comparing Quantities Class 8 Maths.

## Access Exercise wise NCERT Solutions for Chapter 7 Maths Class 8

 NCERT Solutions of Class 8 Comparing Quantities Exercise Links NCERT Solutions of Class 8 Maths Comparing Quantities Exercise 7.1 NCERT Solutions of Class 8 Maths Comparing Quantities Exercise 7.2 NCERT Solutions of Class 8 Maths Comparing Quantities Exercise 7.3

## Exercises Under NCERT Solutions for Class 8 Maths Chapter 7 Comparing Quantities

### Exercise 7.1:

Introduction to Ratios

• Definition and concept of ratios.

• Solving problems involving the comparison of quantities using ratios.

Introduction to Percentages:

• Definition and conversion between fractions, decimals, and percentages.

• Solving problems related to finding percentages of given quantities.

Increase and Decrease Percentages:

• Understanding how to calculate the increase or decrease in percentage.

• Solving problems involving percentage increase and decrease.

### Exercise 7.2:

Finding the Cost Price and Selling Price:

• Concept of cost price (CP) and selling price (SP).

• Solving problems to find CP and SP using given information.

Profit and Loss Calculations:

• Understanding profit and loss.

• Calculating profit and loss percentages based on CP and SP.

Discount:

• Definition and calculation of discount.

• Solving problems involving discount percentages and final prices.

### Exercise 7.3:

Simple Interest:

• Definition and formula for calculating simple interest.

• Solving problems to find simple interest, principal, rate, and time.

Compound Interest:

• Basic understanding of compound interest.

• Difference between simple and compound interest.

Word Problems on Comparing Quantities:

• Solving various word problems that involve the application of ratios, percentages, profit and loss, and simple interest.

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

### 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: Speed of a cycle $=$ $15$km

Speed of scooter $= $$30km Ratio of the speed of a cycle to the speed of scooter = \dfrac{{15}}{{30}} = \dfrac{1}{2} The required ratio is 1:2. (b) 5m to 10km. Ans: 5m to 10km. Since 1km =$$1000$ m

$\Rightarrow $$\dfrac{{5\;{\text{m}}}}{{10\;{\text{km}}}}\; = \,\dfrac{5}{{10}} \times \dfrac{1}{{1000}} = \dfrac{1}{{2000}} \Rightarrow 1:2000 The required ratio is 1:2000. (c) 50 paise to Rs 5. Ans: 50 paise to Rs 5 Since Rs 1 = 100 paise \Rightarrow \dfrac{{50paise}}{{Rs5}} = \dfrac{{50}}{5} \times \dfrac{1}{{100}} = \dfrac{1}{{10}} \Rightarrow 1:10 The required ratio is 1:10. 2. Convert the following ratios to percentages. (a) 3:4 Ans: 3:4 = \dfrac{3}{4} \Rightarrow$$\dfrac{3}{4} \times \dfrac{{100}}{{100}}$

$= $$0.75 \times 100\% = 75\% The required ratio to percentage is 75\% (b) 2:3 Ans: 2:3 = \dfrac{2}{3} = \dfrac{2}{3} \times \dfrac{{100}}{{100}} = \dfrac{{200}}{3}\% = 66\dfrac{2}{3}\% The required ratio to percentage is 66\dfrac{2}{3}\% 3. 72\% of 25 students are good in mathematics. How many are not good in mathematics? Ans: Total number of students = 25 . Percentage of students are good in mathematics =$$72\%$

Percentage of students who are not good in mathematics  $=$ $(100 - 72)\%$

$\Rightarrow 28\%$

$\therefore$ Number of students who are not good in mathematics $= $$28\% \times 25 \Rightarrow \dfrac{{28}}{{100}} \times 25 \Rightarrow \dfrac{{28}}{4} \Rightarrow 7 Students are not good in mathematics = 7 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: The total number of matches won by the football team = 10. Percentage of team = 40\% The total number of matches played by the team = ? The total number of matches played by the team \Rightarrow 40\% \times x = 10 \Rightarrow \dfrac{{40}}{{100}} \times x = 10 \Rightarrow x = 10 \times \dfrac{{100}}{{40}} \Rightarrow x = \dfrac{{100}}{4} \Rightarrow x = 25 The total number of matches played by the team = 25. 5. If Chameli had Rs .600 left after spending 75% of her money, how much did she have in the beginning? Ans:Chameli’s money after spend = 600 Percentage of money after spend = 75\% Beginning amount of chameli = ? Percentage of beginning amount = \left( {100{\text{ }} - {\text{ }}75} \right)\% \qquad = 25\% Beginning amount of chameli \Rightarrow 25\% \times x = 600 \Rightarrow \left( {\dfrac{{25}}{{100}}} \right) \times x = 600 \Rightarrow \left( {\dfrac{1}{4}} \right) \times x = 600 \Rightarrow x = 600 \times 4 \Rightarrow x = 2400 Beginning amount of chameli = 2400. 6. If 60\% people in city like cricket,30\% like football and the remaining like other games, then what per cent 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. Ans: Total number of people in city = 50lakh Percentage of people like cricket = 60\% Percentage of people like football = 30\% Percentage of people like other games = ? Number of people like each type of game = ? Percentage of people like other games = \left( {100 - 60 - 30} \right)\% = \left( {100 - 90} \right)\% = 10\% Percentage of people like other games = 10\% Number of people like cricket = \left( {60\% \times 50} \right) = \left( {\dfrac{{60}}{{100}} \times 50} \right) = \dfrac{{60}}{2} = 30lakh Number of people like cricket = 30lakh Number of people like football = \left( {30\% \times 50} \right) = \left( {\dfrac{{30}}{{100}} \times 50} \right) = \dfrac{{30}}{2} = 15lakh Number of people like football = 15lakh Number of people like other games = \left( {10\% \times 50} \right) = \left( {\dfrac{{10}}{{100}} \times 50} \right) = \dfrac{{10}}{2} = 5lakh. Number of people like other games = 5lakh. ### Exercise 7.2 1. During a sale, a shop offered a discount of 10\% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs 1450 and two shirts marked at Rs 850 each? Ans: Discount percentage = 10\% Price of pair jeans = Rs.1450 Price of shirt = Rs. 850 Formula: Discount = Marked price - Sale price. One shirt price = Rs. 850 Two shirt price = 2 \times Rs. 850 \Rightarrow Rs. 1,700 Total marked price = Rs. \left( {1,450 + 1,700} \right) = Rs. 3,150 Discount = Rs. \left( {10\% \times 3150} \right) = Rs. \left( {\dfrac{{10}}{{100}} \times 3150} \right) Discount = Rs. 315. Discount = Total Marked price - Sale price \Rightarrow Rs 315 = Rs 3150 − Sale price \Rightarrow Sale price = Rs \left( {3150 - 315} \right) \Rightarrow Sale price = Rs 2835 Customer paid = Rs 2835. 2. The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12\% . Find the amount that Vinod will have to pay if he buys it. Ans: Price of TV = Rs. 13,000. Sales tax percentage = 12\% Vinod have to pay = ? if Rs.100, then Tax to be pay is Rs. 12. when Rs. 13,000 Tax to be pay = \left( {\dfrac{{12}}{{100}} \times 13,000} \right) Tax to be pay = 12 \times 130 Tax to be pay = Rs. 1,560. Vinod have to pay = price of TV + Tax to be pay = Rs. 13,000$$ +$ Rs. $1560$

$=$ Rs. $14560$

Vinod have to pay$=$ Rs. $14560$.

3. Arun bought a pair of skates at a sale where the discount given was $20\%$. If the amount he pays is Rs $1,600$. find the marked price.

Ans: Discount in skates $= 20\%$

Total amount $= 1,600$

Marked price $= x$

Formula:

Discount percent$= \left( {\dfrac{{Discount}}{{Marked{\text{ }}price}}} \right) \times 100$

Discount percent $= \left( {\dfrac{{Discount}}{{Marked{\text{ }}price}}} \right) \times 100$

$\Rightarrow 20 = \left( {\dfrac{{Discount}}{x}} \right) \times 100$

Discount $= \dfrac{{20 \times x}}{{100}}$

Discount $= \dfrac{{1 \times x}}{5}$

Discount $=$ Marked price $-$ Total amount

$\Rightarrow \dfrac{{1 \times x}}{5}$$= x - 1600 \Rightarrow 1600 = x - \dfrac{1}{5}x \Rightarrow 1600 = \dfrac{{5x - x}}{5} \Rightarrow 1600 = \dfrac{{4x}}{5} \Rightarrow \dfrac{{1600 \times 5}}{4} = x \Rightarrow x = 400 \times 5 \Rightarrow x = 2000 Marked price = 2000. 4. I purchased a hair-dryer for Rs 5,400 including 8\% VAT. Find the price before VAT was added. Ans: Hair-dryer rate include VAT = 5,400 Tax percentage = 8\% Rate before VAT = ? VAT = 8\% If VAT without Rs.100, then price is Rs. 108 when Rs. 5400 Rate before VAT = \left( {\dfrac{{100}}{{108}} \times 5400} \right) Rate before VAT = 100 \times 50 Rate before VAT = Rs. 5000. 5. An article was purchased for ₹1239 including GST of 18%. Find the price of the article before GST was added? Ans: Let’s assume the price of the article before GST as ₹x. Given that the article was purchased for 1239 rupees, including GST of 18%, so we can write the equation as x + GST = 1239 ….(1) We know that GST is 18% of the price before GST, so: GST = 0.18x Substituting this into (1) x + 0.18x = 1239 1.18x = 1239 x = \frac{{1239}}{{1.18}} x = 1050 So, the price of the article before GST was added is approximately 1050 rupees. ### Exercise 7.3 1. The population of a place increased to 54000 in 2003 at a rate of 5\% per annum (i) find the population in 2001 (ii) what would be its population in 2005? Ans: Population in the year 2003$$ = 54,000$

(i) $54000$ $=$population in 2001 $\times$ ${\left( {1 + \dfrac{5}{{100}}} \right)^2}$

$54000$$= population in 2001 \times$${\left( {\dfrac{{100 + 5}}{{100}}} \right)^2}$

$54000$$= population in 2001 \times$${\left( {\dfrac{{105}}{{100}}} \right)^2}$

$54000$$= population in 2001 \times$${\left( {1.05} \right)^2}$

$54000$$= population in 2001 \times$$1.1025$

$\dfrac{{54000}}{{1.1025}}$$= population in 2001 population in 2001 = 48979.591 (ii) population in 2005 population in 2001 =$$54000{\left( {1 + \dfrac{5}{{100}}} \right)^2}$

population in 2001 $= 54000$${\left( {\dfrac{{100 + 5}}{{100}}} \right)^2}$

population in 2001  $= 54000{\left( {\dfrac{{105}}{{100}}} \right)^2}$

population in 2001 $= 5400{\left( {1.05} \right)^2}$

population in 2001 $= 54000 \times 1.1025$

population in 2001 $= 59.535$

2. In a laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5%  per hour. Find the bacteria at the end of 2 hours if the count was initially $5,06,000$.

Ans:  Initial count of bacteria $= 5,06,000$

Bacteria at the end of $2$ hours

$= 506000{\left( {1 + \dfrac{{2.5}}{{100}}} \right)^2}$

$= 506000{\left( {1 + 0.025} \right)^2}$

$= 506000{\left( {1.025} \right)^2}$

$= 506000\left( {1.050625} \right)$

$= 531616.25$(approximately)

The count of bacteria at the end of 2 hours$= 531616.25$.

3. A scooter was bought at Rs $42,000$. Its value depreciated at the rate of $8\%$ per annum. Find its value after one year.

Ans:  Principal (P) $=$ Rs $42,000$

Rate(R)             $=$ $8\%$ per annum .

Number(n)      $=$ $1$ year.

Formula:

S.I $= \dfrac{{P \times R \times T}}{{100}}$

S.I $=$ Rs $\left( {\dfrac{{42000 \times 8 \times 1}}{{100}}} \right)$

S.I $=$ Rs $8 \times 420$

S.I $=$ Rs $3360$.

Value after $1$ year $=$ Rs. $\left( {42000 - 3360} \right)$

$=$ Rs. $38,640$.

## Overview of Deleted Syllabus for CBSE Class 8 Comparing Quantities Maths Chapter 7

 Chapter Dropped Topics Comparing Quantities 7.2:  Finding the Increase or decrease per cent. 7.4: Prices related to buying and selling. 7.4.1: Finding cost price/selling price, profit%/loss%. 7.8: Rate compounded annually or halfyearly.

## Class 8 Maths Chapter 7: Exercises Breakdown

 Chapter 7 -  Comparing Quantities Exercises in PDF Format Exercise 7.1 6 Questions with Solutions (Short answer type) Exercise 7.2 5 Questions with Solutions (Short answer type) Exercise 7.3 3 Questions with Solutions (Short answer type)

## Conclusion

The NCERT Class 8th Maths Chapter 7, "Comparing Quantities," teaches fundamental mathematical concepts like ratios, percentages, and profit and loss. It emphasizes practical skills like discount calculation, sales price estimation, and understanding simple and compound interest. Students should master percentage calculations and conversion between percentages, fractions, and decimals for exams and real-life financial literacy. The chapter introduces concepts like compound interest through clear examples and practice problems, ensuring students understand compounded growth.

## Other Study Material for CBSE Class 8 Maths Chapter 7

 Sr. No Important Links for Chapter 7 Comparing Quantities 1. Class 8 Comparing Quantities Important Questions 2. Class 8 Comparing Quantities Revision Notes 3. Class 8 Comparing Quantities NCERT Exemplar Solution 4. Class 8 Comparing Quantities Formula

## 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.

## FAQs on NCERT Solutions for Class 8 Maths Chapter 7 Comparing Quantities

1. Define ratio.

A ratio means comparing two quantities of similar units. A ratio of two quantities of the same unit is derived by dividing one quantity by the other.

2. Define interest.

Interest is the extra money paid by the post offices or banks on the money deposited with them. Interest is also paid by the people when they borrow money.

3. What is known as the conversion period?

The time period after which the interest is added each time to form a new principal is known as the conversion period.

4. What is known as overhead expenses?

5. What is the full form of GST?

GST stands for Goods and Services Tax and is imposed on the supply of goods or services or both.

6. Where can I find NCERT Solutions for Chapter 8 “Comparing Quantities” of Class 8 Maths?

Students can easily find NCERT Solutions for Chapter 8 “Comparing Quantities” of Class 8 Maths on the internet. NCERT Solutions for Class 8 maths are available at free of cost on the Vedantu website and on the Vedantu app. Students can download NCERT Solutions free of cost. All Solutions are explained properly. They can click on this NCERT Solutions for Chapter 8 of Class 8 Maths to download solutions. NCERT Solutions can help students to prepare well for their exams. They can understand the concepts given in Chapter 8 easily.

7. What is the principle of comparing quantities in Class 8 Maths Chapter 7 PDF?

In Class 8 Maths Chapter 7 PDF, the principle of comparing quantities involves analysing the relationship between different items or amounts to understand their differences or similarities. This often includes looking at percentages, ratios, proportions, or growth rates to determine how one quantity relates to another.

8. What are the rules for comparing quantities in Class 8 Maths Chapter 7 PDF?

Rules for comparing quantities typically involve using a consistent basis for comparison, such as keeping the units the same or converting them to a common format. Other rules include comparing percentages to understand relative differences, using ratios and proportions to find equivalences, and applying algebraic methods to solve problems involving quantities.

9. How many exercises are there in comparing quantities?

The number of exercises in Class 8 Maths Chapter 7 can vary slightly depending on the edition of the NCERT textbook. Typically, there are around 3 to 4 exercises, each designed to help students practice and master different aspects of comparing quantities, including percentage, profit and loss, and compound interest.

10. What is the full form of CI in comparing quantities?

The word "CI" in the context of comparing quantities stands for Compound Interest. This refers to the calculation of interest where the earned interest is added to the principal sum, so that from that moment on, the interest that has been added also earns interest. This method leads to a significantly increased total return over time compared to simple interest, where interest is calculated only on the principal amount.

11. Which chart is used to compare quantities in Class 8 Maths Comparing Quantities?

Various charts can be used to compare quantities, but one common type is the bar chart. Bar charts are particularly useful for comparing quantities across different categories or groups visually, allowing for quick comparison of sizes, amounts, or changes over time.

12. What does comparing quantities mean in Class 8 Maths Comparing Quantities?

In Maths, comparing quantities means evaluating and determining the relationship between two or more quantities. This might involve calculations to find out which quantity is greater, how many times one quantity is of another, or what percentage one quantity represents of another.

13. What are the topics covered in Class 8 Maths Comparing Quantities?

Class 8 Maths Comparing Quantities covers several key concepts:

• Understanding and calculating percentages.

• Applying percentages to find increases or decreases, like profit and loss.

• Working with simple and compound interest calculations.

• Understanding ratios and proportions in different contexts.

• Using conversions for comparing different units.

• Solving real-world problems using the concepts of percentages, ratios, and interest.