Two ratios are said to be in proportion if they are equal. Proportions compare two ratios and determine if they are equivalent.

What is the Difference Between Ratio and Proportion?

Ratio compares two quantities by division. It shows how many times one quantity is contained in the other. Proportion states that the two ratios are equal. It compares the relationship between four quantities.

What is an Equivalent Ratio?

Equivalent ratios are two or more ratios that express the same relationship between numbers, achieved by multiplying or dividing both parts of a ratio by the same non-zero number.

CBSE Notes

Class 7

Maths

Chapter 7 Comparing Quantities

Frequently Asked Questions

CBSE Class 7

The CBSE Class 7 exam is an important milestone in a student's educational journey and is conducted under the Central Board of Secondary Education guidelines...

CBSE Class 7 Syllabus

The CBSE Class 7 syllabus is crucial for organized learning and exam preparation, providing a clear understanding of...

CBSE Class 7 Notes

CBSE Class 7 Notes are important for understanding the basic concepts in all subjects and building a strong foundation for advance classes.

NCERT Solutions Class 7

The questions and illustrations in the NCERT Class 7 Science textbook have comprehensive explanations and answers...

CBSE Exam

CBSE is a national-level board of education in India, responsible for public and private school education, and is managed by the Gove...

Important CBSE Science Topics

Science is, therefore, a systematic enterprise that organizes and builds testable explanations and predic...

Important CBSE Maths Topics

Mathematics is the study of patterns, structure, and relationships, rooted in fundamental practices like counting,...

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CBSE Notes Class 7 Maths Chapter 7 - Comparing Quantities

Comparing Quantities involves using ratios, percentages, and proportions to compare two or more values. A ratio shows how many times one value contains another, while percentages express a value as a fraction of 100. Proportion compares two equal ratios. Concepts like profit, loss, and simple interest help in comparing financial quantities effectively.

1.0Download CBSE Class 7 Maths Chapter 7 Comparing Quantities Notes : Free PDF

Download CBSE Class 7 Maths Chapter 7 – Comparing Quantities Notes in a free and easy-to-access PDF format. These notes provide a clear summary of key concepts such as percentages, profit and loss, simple interest, and ratio and proportion.Strengthen your understanding of CBSE Class 7 Maths topics with well-organized content designed to support effective learning. Get your free PDF now!

Class 7 Maths Chapter 7 Revision Notes:

2.0Comparing Quantities: An Introduction

To compare two quantities, ensure both quantities are expressed in the same units. Here are some examples:

Joe’s height is 150 cm, while Tom’s height is 100 cm. The ratio of Joe's height to Tom's is:

$Ratio = \frac{150}{100} = \frac{3}{2} or 3 : 2$

The ratio of 3 km to 30 m is:

$\frac{3 km}{30 m} = \frac{3000 m}{30 m} = 100 : 1$

3.0Ratios

A ratio compares two quantities by showing how many times one value contains or is contained within the other. For instance, if there are 4 girls and 7 boys in a class, the ratio of girls to boys is 4:7.

Equivalent Ratios:

Multiplying both the numerator and denominator of a ratio by the same non-zero number gives an equivalent ratio. For example:

$\frac{2}{3} and \frac{4}{6}$ are equivalent ratios.

4.0Proportions

When two ratios are equal, they are said to be in proportion. This can be represented as either "::" or "=". For example:

$2 : 3 :: 6 : 9 or \frac{2}{3} = \frac{6}{9} .$

Also Read: Ratio and Proportion

5.0Calculating Percentage Increase or Decrease

To find the percentage change, use the following formula:

$Percentage Change = \frac{Change in Value}{Original Value} \times 100$

For example, if the price of a book increases from ₹20 to ₹25, the percentage increase is:

Change = 25 – 20 = 5,

$Percentage Increase = \frac{5}{20} \times 100 = 25%$

6.0Percentages

Percentages represent a ratio as a fraction of 100. For example:

$40% = \frac{40}{100}, 25% = \frac{25}{100}$

If the denominator is not 100, convert the fraction to one that has a denominator of 100. For example:

$\frac{3}{5} = \frac{60}{100} = 60%$

7.0Converting Between Decimals, Fractions, and Percentages

To change a decimal into a percentage, multiply the by 100. For example, 0.44 becomes 44%.
To convert a fraction to a percentage, first make its denominator 100 and then express it as a percentage.

8.0Estimation and Interpretation Using Percentages

Percentages help interpret data more effectively. For example, if 60% of 200 chocolates were given to Joe and 40% to Tom:

$Joe’s share = \frac{60}{100} \times 200 = 120 chocolates, Tom’s share = \frac{40}{100} \times 200 = 80 chocolates.$

Ratios can also be expressed as percentages to enhance understanding of certain situations.

Profit Percentage:

Profit Percentage is the percentage of profit made on the cost price of an item. It is calculated using the formula:

$Profit Percentage = (\frac{Profit}{Cost Price}) \times 100$

Since Profit = Selling Price – Cost Price, we can express the formula as:

$Profit Percentage = (\frac{SP - CP}{CP}) \times 100$

This formula helps to determine the percentage of gain in relation to the original cost price.

Loss Percentage

Loss Percentage is the percentage of loss incurred on the cost price of an item. It is calculated using the formula:

$Loss Percentage = (\frac{Loss}{Cost Price}) \times 100$

Since Loss = Cost Price – Selling Price, the formula becomes:

$Loss Percentage = (\frac{CP - SP}{CP}) \times 100$

This gives the percentage of loss relative to the cost price.

9.0Prices Related to Buying and Selling

When discussing prices of items, there are two key terms:

Selling Price (SP): This is the price at which an item is sold to a buyer.
Cost Price (CP): This represents the original price at which an item was purchased.

To calculate the profit or loss made from a sale:

Profit = Selling Price – Cost Price (when SP > CP).
Loss = Cost Price – Selling Price (when CP > SP).

If SP is equal to CP, there is neither a profit nor a loss.

10.0Simple and Compound Interest

The principal (P) is the initial sum borrowed.
Interest is the extra amount paid to the lender.
The total amount to be repaid (A) is: Amount = Principal + Interest.
Simple Interest (SI) is calculated using:

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

where P is the principal, R is the rate of interest, and T is the time in years.

For example, if P = ₹200, R = 10%, and T = 3 years:

S I $= \frac{200 \times 10 \times 3}{100}$ = ₹60.

Thus, the total amount to be paid is:

Amount = Principal + Simple Interest

= 200 + 60 = ₹260.

11.0Solved Examples on Comparing Quantities

Example 1: Compare 3 kilometers and 200 meters using ratios.

Solution:

First, convert kilometers to meters.

3 km = 3000 meters.

Now, the ratio is:

$\frac{3000}{200} = 15 : 1$

Thus, the ratio of 3 km to 200 m is 15:1.

Example 2: Convert the fraction $\frac{3}{4}$ into a percentage.

Solution:

To convert a fraction to a percentage, multiply it by 100:

$\frac{3}{4} \times 100 = 75%$

Thus, $\frac{3}{4}$ as a percentage is 75%.

Example 3: Find 20% of 250.

Solution:

To find 20% of 250, use the formula:

$Percentage of a number = \frac{percentage}{100} \times number$

$20% of 250 = \frac{20}{100} \times 250 = 50$

Thus, 20% of 250 is 50.

Example 4: A shopkeeper buys a toy for ₹400 and sells it for ₹500. What is the profit percentage?

Solution:

First, calculate the profit:

Profit = Selling Price – Cost Price

= ₹ 500 – ₹ 400 = ₹100.

Now, calculate the profit percentage:

$Profit Percentage = (\frac{Profit}{Cost Price}) \times 100 = (\frac{100}{400}) \times 100 = 25% .$

Thus, the profit percentage is 25%.

Example 5: A person buys a book for ₹250 and sells it for ₹200. What is the loss percentage?

Solution:

First, calculate the loss:

Loss = Cost Price – Selling Price

= ₹ 250 – ₹200 = ₹50.

Now, calculate the loss percentage:

$Loss Percentage = (\frac{Loss}{Cost Price}) \times 100 = (\frac{50}{250}) \times 100 = 20% .$

Thus, the loss percentage is 20%.

Example 6: The ratio of girls to boys in a class is 3:5. Find the percentage of girls and boys in the class.

Solution:

Total parts = 3 + 5 = 8.

Percentage of girls:

$\frac{3}{8} \times 100 = 37.5%$

Percentage of boys:

$\frac{5}{8} \times 100 = 62.5%$

Thus, 37.5% of the class are girls and 62.5% are boys.

Example 7: If 6 : 8 :: x : 12, find the value of x.

Solution:

Set up the proportion:

$\frac{6}{8} = \frac{x}{12}$

Cross-multiply:

$6 \times 12 = 8 \times x .$

Simplifying:

$72 = 8 x \Rightarrow x = \frac{72}{8} = 9$

Thus, x = 9.

Example 8: Convert 0.75 into a percentage.

Solution:

To convert a decimal to a percentage, multiply it by 100:

$0.75 \times 100 = 75%$

Thus, 0.75 as a percentage is 75%.

12.0Practice Questions on Comparing Quantities

Convert the Following Fractions into Percentages:

$\frac{2}{5}$
$\frac{5}{6}$

Find the Ratio of the Following Quantities in Same Units:

5 kg to 200 g
6 hours to 90 minutes
₹500 to ₹2000

Percentage of a Number:

Find 15% of 300.
Find 45% of 800.

A shopkeeper buys a mobile phone for ₹15,000 and sells it for ₹18,000. Find the profit percentage.
If a car is bought for ₹3,00,000 and sold for ₹2,70,000, find the loss percentage.
In a school, 65% of the students are boys. If the total number of students is 600, how many boys are there in the school? Convert it into percentage.
The ratio of green balls to blue balls in a box is 4:6. What percentage of balls are green and what percentage are blue?

13.0Sample Questions on Comparing Quantities

How Do We Find the Percentage of a Given Quantity?

Ans: To find the percentage of a quantity, multiply the given quantity by the percentage value and divide it by 100.

Formula:

$Percentage of a quantity = \frac{Percentage value}{100} \times Quantity$

How Do We Convert a Fraction to a Percentage?

Ans: To convert a fraction into a percentage, multiply the fraction by 100.

Formula:

$Percentage = \frac{Numerator}{Denominator} \times 100$

What is the Formula for Simple Interest?

Ans: The formula for Simple Interest (SI) is:

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

where:

P = Principal (initial amount)

R = Rate of interest

T = Time (in years)

14.0Key Features of Class 7 Maths Chapter 7 - Comparing Quantities

Clear formulas and methods to calculate profit, loss, and discount in commercial transactions.
Step-by-step explanation of how to calculate simple interest with real-world examples.
Summarized key points and formulas at the end of the chapter for fast and effective revision.
Understanding how percentages are used to compare quantities and solve problems.
Detailed coverage of ratios, proportions, and their applications in solving various problems.

Chapter-wise CBSE Notes for Class 7 Maths:

Class 7 Maths Chapter 1 - Integers Notes

Class 7 Maths Chapter 2 - Fractions and Decimals Notes

Class 7 Maths Chapter 3 - Data Handling Notes

Class 7 Maths Chapter 4 - Simple Equations Notes

Class 7 Maths Chapter 5 - Lines And Angles Notes

Class 7 Maths Chapter 6 - The Triangles and its Properties Notes

Class 7 Maths Chapter 7 - Comparing Quantities Notes

Class 7 Maths Chapter 8 - Rational Numbers Notes

Class 7 Maths Chapter 9 - Perimeter And Area Notes

Class 7 Maths Chapter 10 - Algebraic Expressions Notes

Class 7 Maths Chapter 11 - Exponents And Powers Notes

Class 7 Maths Chapter 12 - Symmetry Notes

Class 7 Maths Chapter 13 - Visualising Solid Shapes Notes

Chapter-wise NCERT Solutions for Class 7 Maths:-

Chapter 1: Integers

Chapter 2: Fractions and Decimals

Chapter 3: Data Handling

Chapter 4: Simple Equations

Chapter 5: Lines and Angles

Chapter 6: The Triangle and its Properties

Chapter 7: Comparing Quantities

Chapter 8: Rational Numbers

Chapter 9: Perimeter and Area

Chapter 10: Algebraic Expressions

Chapter 11: Exponents and Powers

Chapter 12: Symmetry

Chapter 13: Visualising Solid Shapes

Frequently Asked Questions

CBSE Class 7

The CBSE Class 7 exam is an important milestone in a student's educational journey and is conducted under the Central Board of Secondary Education guidelines...

CBSE Class 7 Syllabus

The CBSE Class 7 syllabus is crucial for organized learning and exam preparation, providing a clear understanding of...

CBSE Class 7 Notes

CBSE Class 7 Notes are important for understanding the basic concepts in all subjects and building a strong foundation for advance classes.

NCERT Solutions Class 7

The questions and illustrations in the NCERT Class 7 Science textbook have comprehensive explanations and answers...

CBSE Exam

CBSE is a national-level board of education in India, responsible for public and private school education, and is managed by the Gove...

Important CBSE Science Topics

Science is, therefore, a systematic enterprise that organizes and builds testable explanations and predic...

Important CBSE Maths Topics

Mathematics is the study of patterns, structure, and relationships, rooted in fundamental practices like counting,...

Join ALLEN!

(Session 2026 - 27)

Name

Mobile Number

Class

Choose class

Goal

Choose your goal

Preferred Programs

Preferred Mode

State

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I agree to

I authorise ALLEN Career Institute Pvt Ltd to send me regular updates via Phone calls, Whatsapp, SMS, Robocalls (Automated Calls), Emails, or on postal address.

CBSE Notes Class 7 Maths Chapter 7 - Comparing Quantities

Comparing Quantities involves using ratios, percentages, and proportions to compare two or more values. A ratio shows how many times one value contains another, while percentages express a value as a fraction of 100. Proportion compares two equal ratios. Concepts like profit, loss, and simple interest help in comparing financial quantities effectively.

1.0Download CBSE Class 7 Maths Chapter 7 Comparing Quantities Notes : Free PDF

Download CBSE Class 7 Maths Chapter 7 – Comparing Quantities Notes in a free and easy-to-access PDF format. These notes provide a clear summary of key concepts such as percentages, profit and loss, simple interest, and ratio and proportion.Strengthen your understanding of CBSE Class 7 Maths topics with well-organized content designed to support effective learning. Get your free PDF now!

Class 7 Maths Chapter 7 Revision Notes:

2.0Comparing Quantities: An Introduction

To compare two quantities, ensure both quantities are expressed in the same units. Here are some examples:

Joe’s height is 150 cm, while Tom’s height is 100 cm. The ratio of Joe's height to Tom's is:

$Ratio = \frac{150}{100} = \frac{3}{2} or 3 : 2$

The ratio of 3 km to 30 m is:

$\frac{3 km}{30 m} = \frac{3000 m}{30 m} = 100 : 1$

3.0Ratios

A ratio compares two quantities by showing how many times one value contains or is contained within the other. For instance, if there are 4 girls and 7 boys in a class, the ratio of girls to boys is 4:7.

Equivalent Ratios:

Multiplying both the numerator and denominator of a ratio by the same non-zero number gives an equivalent ratio. For example:

$\frac{2}{3} and \frac{4}{6}$ are equivalent ratios.

4.0Proportions

When two ratios are equal, they are said to be in proportion. This can be represented as either "::" or "=". For example:

$2 : 3 :: 6 : 9 or \frac{2}{3} = \frac{6}{9} .$

Also Read: Ratio and Proportion

5.0Calculating Percentage Increase or Decrease

To find the percentage change, use the following formula:

$Percentage Change = \frac{Change in Value}{Original Value} \times 100$

For example, if the price of a book increases from ₹20 to ₹25, the percentage increase is:

Change = 25 – 20 = 5,

$Percentage Increase = \frac{5}{20} \times 100 = 25%$

6.0Percentages

Percentages represent a ratio as a fraction of 100. For example:

$40% = \frac{40}{100}, 25% = \frac{25}{100}$

If the denominator is not 100, convert the fraction to one that has a denominator of 100. For example:

$\frac{3}{5} = \frac{60}{100} = 60%$

7.0Converting Between Decimals, Fractions, and Percentages

To change a decimal into a percentage, multiply the by 100. For example, 0.44 becomes 44%.
To convert a fraction to a percentage, first make its denominator 100 and then express it as a percentage.

8.0Estimation and Interpretation Using Percentages

Percentages help interpret data more effectively. For example, if 60% of 200 chocolates were given to Joe and 40% to Tom:

$Joe’s share = \frac{60}{100} \times 200 = 120 chocolates, Tom’s share = \frac{40}{100} \times 200 = 80 chocolates.$

Ratios can also be expressed as percentages to enhance understanding of certain situations.

Profit Percentage:

Profit Percentage is the percentage of profit made on the cost price of an item. It is calculated using the formula:

$Profit Percentage = (\frac{Profit}{Cost Price}) \times 100$

Since Profit = Selling Price – Cost Price, we can express the formula as:

$Profit Percentage = (\frac{SP - CP}{CP}) \times 100$

This formula helps to determine the percentage of gain in relation to the original cost price.

Loss Percentage

Loss Percentage is the percentage of loss incurred on the cost price of an item. It is calculated using the formula:

$Loss Percentage = (\frac{Loss}{Cost Price}) \times 100$

Since Loss = Cost Price – Selling Price, the formula becomes:

$Loss Percentage = (\frac{CP - SP}{CP}) \times 100$

This gives the percentage of loss relative to the cost price.

9.0Prices Related to Buying and Selling

When discussing prices of items, there are two key terms:

Selling Price (SP): This is the price at which an item is sold to a buyer.
Cost Price (CP): This represents the original price at which an item was purchased.

To calculate the profit or loss made from a sale:

Profit = Selling Price – Cost Price (when SP > CP).
Loss = Cost Price – Selling Price (when CP > SP).

If SP is equal to CP, there is neither a profit nor a loss.

10.0Simple and Compound Interest

The principal (P) is the initial sum borrowed.
Interest is the extra amount paid to the lender.
The total amount to be repaid (A) is: Amount = Principal + Interest.
Simple Interest (SI) is calculated using:

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

where P is the principal, R is the rate of interest, and T is the time in years.

For example, if P = ₹200, R = 10%, and T = 3 years:

S I $= \frac{200 \times 10 \times 3}{100}$ = ₹60.

Thus, the total amount to be paid is:

Amount = Principal + Simple Interest

= 200 + 60 = ₹260.

11.0Solved Examples on Comparing Quantities

Example 1: Compare 3 kilometers and 200 meters using ratios.

Solution:

First, convert kilometers to meters.

3 km = 3000 meters.

Now, the ratio is:

$\frac{3000}{200} = 15 : 1$

Thus, the ratio of 3 km to 200 m is 15:1.

Example 2: Convert the fraction $\frac{3}{4}$ into a percentage.

Solution:

To convert a fraction to a percentage, multiply it by 100:

$\frac{3}{4} \times 100 = 75%$

Thus, $\frac{3}{4}$ as a percentage is 75%.

Example 3: Find 20% of 250.

Solution:

To find 20% of 250, use the formula:

$Percentage of a number = \frac{percentage}{100} \times number$

$20% of 250 = \frac{20}{100} \times 250 = 50$

Thus, 20% of 250 is 50.

Example 4: A shopkeeper buys a toy for ₹400 and sells it for ₹500. What is the profit percentage?

Solution:

First, calculate the profit:

Profit = Selling Price – Cost Price

= ₹ 500 – ₹ 400 = ₹100.

Now, calculate the profit percentage:

$Profit Percentage = (\frac{Profit}{Cost Price}) \times 100 = (\frac{100}{400}) \times 100 = 25% .$

Thus, the profit percentage is 25%.

Example 5: A person buys a book for ₹250 and sells it for ₹200. What is the loss percentage?

Solution:

First, calculate the loss:

Loss = Cost Price – Selling Price

= ₹ 250 – ₹200 = ₹50.

Now, calculate the loss percentage:

$Loss Percentage = (\frac{Loss}{Cost Price}) \times 100 = (\frac{50}{250}) \times 100 = 20% .$

Thus, the loss percentage is 20%.

Example 6: The ratio of girls to boys in a class is 3:5. Find the percentage of girls and boys in the class.

Solution:

Total parts = 3 + 5 = 8.

Percentage of girls:

$\frac{3}{8} \times 100 = 37.5%$

Percentage of boys:

$\frac{5}{8} \times 100 = 62.5%$

Thus, 37.5% of the class are girls and 62.5% are boys.

Example 7: If 6 : 8 :: x : 12, find the value of x.

Solution:

Set up the proportion:

$\frac{6}{8} = \frac{x}{12}$

Cross-multiply:

$6 \times 12 = 8 \times x .$

Simplifying:

$72 = 8 x \Rightarrow x = \frac{72}{8} = 9$

Thus, x = 9.

Example 8: Convert 0.75 into a percentage.

Solution:

To convert a decimal to a percentage, multiply it by 100:

$0.75 \times 100 = 75%$

Thus, 0.75 as a percentage is 75%.

12.0Practice Questions on Comparing Quantities

Convert the Following Fractions into Percentages:

$\frac{2}{5}$
$\frac{5}{6}$

Find the Ratio of the Following Quantities in Same Units:

5 kg to 200 g
6 hours to 90 minutes
₹500 to ₹2000

Percentage of a Number:

Find 15% of 300.
Find 45% of 800.

A shopkeeper buys a mobile phone for ₹15,000 and sells it for ₹18,000. Find the profit percentage.
If a car is bought for ₹3,00,000 and sold for ₹2,70,000, find the loss percentage.
In a school, 65% of the students are boys. If the total number of students is 600, how many boys are there in the school? Convert it into percentage.
The ratio of green balls to blue balls in a box is 4:6. What percentage of balls are green and what percentage are blue?

13.0Sample Questions on Comparing Quantities

How Do We Find the Percentage of a Given Quantity?

Ans: To find the percentage of a quantity, multiply the given quantity by the percentage value and divide it by 100.

Formula:

$Percentage of a quantity = \frac{Percentage value}{100} \times Quantity$

How Do We Convert a Fraction to a Percentage?

Ans: To convert a fraction into a percentage, multiply the fraction by 100.

Formula:

$Percentage = \frac{Numerator}{Denominator} \times 100$

What is the Formula for Simple Interest?

Ans: The formula for Simple Interest (SI) is:

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

where:

P = Principal (initial amount)

R = Rate of interest

T = Time (in years)

14.0Key Features of Class 7 Maths Chapter 7 - Comparing Quantities

Clear formulas and methods to calculate profit, loss, and discount in commercial transactions.
Step-by-step explanation of how to calculate simple interest with real-world examples.
Summarized key points and formulas at the end of the chapter for fast and effective revision.
Understanding how percentages are used to compare quantities and solve problems.
Detailed coverage of ratios, proportions, and their applications in solving various problems.

Chapter-wise CBSE Notes for Class 7 Maths:

Class 7 Maths Chapter 1 - Integers Notes

Class 7 Maths Chapter 2 - Fractions and Decimals Notes

Class 7 Maths Chapter 3 - Data Handling Notes

Class 7 Maths Chapter 4 - Simple Equations Notes

Class 7 Maths Chapter 5 - Lines And Angles Notes

Class 7 Maths Chapter 6 - The Triangles and its Properties Notes

Class 7 Maths Chapter 7 - Comparing Quantities Notes

Class 7 Maths Chapter 8 - Rational Numbers Notes

Class 7 Maths Chapter 9 - Perimeter And Area Notes

Class 7 Maths Chapter 10 - Algebraic Expressions Notes

Class 7 Maths Chapter 11 - Exponents And Powers Notes