Formulas of Comparing Quantities Explained Simply

Tanya GuptaAt Planet Spark, I believe in making math fun and accessible for all students. My teaching approach focuses on building a strong foundation, fostering problem-solving skills, and encouraging curiosity and creativity. By making math relevant and engaging, I empower students to develop a lifelong love for learning and excel in this essential subject.

Last Updated At: 17 Jan 2026

12 min read

Table of Contents

What Is Comparing Quantities in Maths
Key Concepts Used in Comparing Quantities
Formulas of Comparing Quantities Explained Simply
How to Apply Comparing Quantities Formulas Step by Step
Success Story Spotlight
Common Mistakes Students Make in Comparing Quantities
Simple Tricks to Remember Comparing Quantities Formulas
Why Concept-Based Learning Works Better Than Rote Learning
Comparing Quantities Maths Examples
Real-Life Applications of Comparing Quantities
Step-by-Step Examples of Comparing Quantities Problems
Tips for Parents to Help Children Understand Comparing Quant
How to Check Answers and Avoid Common Errors
How PlanetSpark Helps Children Master Comparing Quantities
Conclusion

Comparing quantities is one of the most important maths topics students learn in middle school, yet it often feels confusing because of too many formulas and word problems. Concepts like percentages, profit, loss, and simple interest can become difficult when children memorise formulas without understanding how they work.

This confusion affects exam performance and confidence. In this article, we explain the formulas of comparing quantities in a simple, concept-based way, using clear steps and everyday examples, so parents can help their children build strong maths foundations with confidence.

What Is Comparing Quantities in Maths

Comparing quantities in maths means looking at two or more values to see how they relate to each other. It helps students understand whether one value is larger, smaller, or equal to another and by how much.

Where Students Use Comparing Quantities in Daily Life

Checking discounts while shopping
Calculating price increases or decreases
Figuring out interest on savings or loans
Comparing scores, marks, or performance in exams

Why This Chapter Is Important for Exams and Real-World Understanding

Understanding comparing quantities goes beyond exams. It helps children make informed decisions in everyday life, such as calculating profits, evaluating deals, or planning budgets. In exams, it is a high-scoring topic because most problems are formula-based and easy to solve once the concepts are clear.

Key Concepts Used in Comparing Quantities

Before diving into formulas, it’s essential to understand the key concepts that form the foundation of comparing quantities.

Ratios and Percentages

Ratios show the relationship between two numbers. For example, if a classroom has 12 boys and 8 girls, the ratio of boys to girls is 12:8 or 3:2.
Percentages represent a part of a whole out of 100. For example, scoring 45 out of 50 marks is 90%.

Increase and Decrease in Value

Increase: When a quantity becomes more than its original value. Example: A toy price rises from ₹200 to ₹250.
Decrease: When a quantity becomes less than its original value. Example: A book originally ₹500 is sold for ₹450.

Understanding Base Value and Comparison Value

Base Value: The original or reference value in a problem. Example: ₹200 is the base when calculating a 20% increase.
Comparison Value: The new or changed value to compare with the base. Example: ₹250 is compared with ₹200 to find the increase.

Grasping these concepts ensures that children can easily apply the formulas for percentages, profit, loss, and simple interest in any problem.

Formulas of Comparing Quantities Explained Simply

Understanding formulas becomes easy when concepts are clear. Here are the main formulas used in comparing quantities, explained with simple examples.

Percentage Formula

Formula:

\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

$Percentage$ $=$ $WholePart$ $$ $\times$ $100$

Example:
A student scores 45 marks out of 50.

\text{Percentage} = \frac{45}{50} \times 100 = 90\%

$Percentage$ $=$ $5045$ $$ $\times$ $100$ $=$ $90%$

This means the student scored 90% of the total marks.

Percentage Increase Formula

Formula:

\text{Percentage Increase} = \frac{\text{New Value – Original Value}}{\text{Original Value}} \times 100

$Percentage Increase$ $=$ $Original ValueNew Value - Original Value$ $$ $\times$ $100$

Example:
A toy costs ₹200 and the price rises to ₹250.

\text{Increase} = 250 – 200 = 50

$Increase$ $=$ $250-200$ $=$ $50$ $\text{Percentage Increase} = \frac{50}{200} \times 100 = 25\%$ $Percentage Increase$ $=$ $20050$ $$ $\times$ $100$ $=$ $25%$

The toy price increased by 25%.

Percentage Decrease Formula

Formula:

\text{Percentage Decrease} = \frac{\text{Original Value – New Value}}{\text{Original Value}} \times 100

$Percentage Decrease$ $=$ $Original ValueOriginal Value - New Value$ $$ $\times$ $100$

Example:
A book originally costs ₹500 and is now sold for ₹450.

\text{Decrease} = 500 – 450 = 50

$Decrease$ $=$ $500-450$ $=$ $50$ $\text{Percentage Decrease} = \frac{50}{500} \times 100 = 10\%$ $Percentage Decrease$ $=$ $50050$ $$ $\times$ $100$ $=$ $10%$

The book price decreased by 10%.

Help your child learn comparing quantities with step-by-step guidance.

Profit Formula

Formula:

\text{Profit} = \text{Selling Price (SP)} – \text{Cost Price (CP)}

$Profit$ $=$ $Selling Price (SP)$ $-$ $Cost Price (CP)$

Example:
A bicycle costs ₹3,000 and is sold for ₹3,500.

\text{Profit} = 3500 – 3000 = 500

$Profit$ $=$ $3500-3000$ $=$ $500$

The profit earned is ₹500.

Profit Percentage:

\text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100 = \frac{500}{3000} \times 100 = 16.67\%

$Profit %$ $=$ $CPProfit$ $$ $\times$ $100$ $=$ $3000500$ $$ $\times$ $100$ $=$ $16.67%$

Loss Formula

Formula:

\text{Loss} = \text{Cost Price (CP)} – \text{Selling Price (SP)}

$Loss$ $=$ $Cost Price (CP)$ $-$ $Selling Price (SP)$

Example:
A laptop costs ₹40,000 but is sold for ₹38,000.

\text{Loss} = 40000 – 38000 = 2000

$Loss$ $=$ $40000-38000$ $=$ $2000$

The loss incurred is ₹2,000.

Loss Percentage:

\text{Loss \%} = \frac{2000}{40000} \times 100 = 5\%

$Loss %$ $=$ $400002000$ $$ $\times$ $100$ $=$ $5%$

Simple Interest Formula

Formula:

\text{SI} = \frac{\text{Principal × Rate × Time}}{100}

$SI$ $=$ $100$ $Principal \times Rate \times Time$ $$

Example:
If ₹10,000 is invested at 5% per year for 2 years:

\text{SI} = \frac{10000 \times 5 \times 2}{100} = 1000

$SI$ $=$ $10010000$ $\times$ $5$ $\times$ $2$ $$ $=$ $1000$

The simple interest earned is ₹1,000.

How to Apply Comparing Quantities Formulas Step by Step

Identify given values – Check the problem for the part, whole, cost price, selling price, or principal.
Choose the correct formula – Decide whether it’s percentage, profit, loss, or interest.
Substitute values – Put the numbers into the formula carefully.
Calculate carefully – Perform the arithmetic step by step to avoid mistakes.
Check the answer – Make sure the result makes sense in the context of the question.

Success Story Spotlight

Success Story: Thaksh, Age 11

Won the ‘taleNt 2025’ competition in Thane
Excelled in all three stages: written exam, interview, and final evaluation
Demonstrated strong problem-solving and communication skills
Achieved success through consistent practice and guidance at PlanetSpark

Thaksh’s journey shows how structured learning and confidence-building help children perform at their best in competitions, exams, and real-life challenges

Common Mistakes Students Make in Comparing Quantities

Even simple formulas can lead to mistakes if students don’t pay attention to the details. Here are some common errors:

Confusing cost price and selling price – Mixing these values leads to wrong profit or loss calculations.
Using the wrong base value – In percentage problems, the original value must always be correctly identified.
Calculation errors in percentages – Skipping steps or dividing incorrectly causes wrong answers.
Rushing through word problems – Misreading the question or missing key details leads to mistakes.

By addressing these errors early, children can solve problems confidently and accurately.

Simple Tricks to Remember Comparing Quantities Formulas

Remembering formulas becomes easier when students link them to practical methods:

Mnemonics for formulas – Short phrases like “SP minus CP gives Profit” help memorise formulas quickly.
Visual methods – Use diagrams, charts, or tables to compare values and understand increases or decreases.
Linking formulas to real-life situations – Relate problems to shopping discounts, bank interest, or exam scores to make formulas meaningful.

These tricks make learning fun and reduce errors while boosting confidence.

Why Concept-Based Learning Works Better Than Rote Learning

Learning maths by understanding concepts is far more effective than memorising formulas without context:

Explains concept-based maths learning – Students learn why formulas work, not just how to apply them.
Improves understanding and confidence – Children solve problems logically, which builds self-assurance in exams and real-life situations.
Long-term benefits for exams and higher classes – Strong conceptual clarity prepares students for more advanced topics in higher grades.

Concept-based learning ensures that children retain knowledge longer and apply it confidently across problems.

Comparing Quantities Maths Examples

Understanding comparing quantities becomes much easier when children see practical examples. Using formulas of comparing quantities Class 8, students can solve problems confidently step by step.

Example 1 – Percentage:
A student scored 36 out of 45 marks.

\text{Percentage} = \frac{36}{45} \times 100 = 80\%

$Percentage$ $=$ $4536$ $$ $\times$ $100$ $=$ $80%$

This shows the student scored 80% of the total marks.

Example 2 – Profit and Loss:
A notebook costs ₹50 and is sold for ₹65.

\text{Profit} = 65 - 50 = 15, \quad \text{Profit \%} = \frac{15}{50} \times 100 = 30\%

$Profit$ $=$ $65$ $-$ $50$ $=$ $15$ $,$ $Profit %$ $=$ $5015$ $$ $\times$ $100$ $=$ $30%$

Example 3 – Percentage Decrease:
A bag originally costs ₹800 and is sold for ₹720.

\text{Percentage Decrease} = \frac{800-720}{800} \times 100 = 10\%

$Percentage Decrease$ $=$ $800800$ $-$ $720$ $$ $\times$ $100$ $=$ $10%$

By practising these formulas of comparing quantities Class 8, children can tackle both exam questions and real-life problems with ease.

Real-Life Applications of Comparing Quantities

Comparing quantities is not just a classroom topic—it helps children understand the world around them. By practising these concepts, children can see how maths applies to everyday life.

Shopping and Discounts: Children can calculate how much they save during a sale using percentages. For example, a toy priced at ₹500 with a 20% discount costs ₹400.
Allowances and Pocket Money: Kids can compare weekly allowance versus expenses to learn budgeting and savings.
Games and Scores: Ratios and percentages help compare scores in sports, video games, or competitions.
Profit and Loss in Small Ventures: Children selling crafts or snacks can calculate profit or loss and understand business basics.

These real-life applications make formulas meaningful and help children relate maths to practical decisions.

Book a free maths demo class for your 7–12 year old today.

Step-by-Step Examples of Comparing Quantities Problems

Here are some simple, solved problems to help children practice:

Example 1: Percentage Problem
A student scored 36 out of 45 marks. Find the percentage.

\text{Percentage} = \frac{36}{45} \times 100 = 80\%

$Percentage$ $=$ $4536$ $$ $\times$ $100$ $=$ $80%$

Example 2: Profit Problem
A notebook costs ₹50 and is sold for ₹65. Find the profit and profit percentage.

\text{Profit} = 65 – 50 = 15

$Profit$ $=$ $65-50$ $=$ $15$ $\text{Profit \%} = \frac{15}{50} \times 100 = 30\%$ $Profit %$ $=$ $5015$ $$ $\times$ $100$ $=$ $30%$

Example 3: Percentage Decrease Problem
A bag originally costs ₹800 and is sold for ₹720. Find the percentage decrease.

\text{Decrease} = 800 – 720 = 80

$Decrease$ $=$ $800-720$ $=$ $80$ $\text{Percentage Decrease} = \frac{80}{800} \times 100 = 10\%$ $Percentage Decrease$ $=$ $80080$ $$ $\times$ $100$ $=$ $10%$

These step-by-step examples help children visualise the calculation process and reinforce conceptual understanding.

Tips for Parents to Help Children Understand Comparing Quantities

Parents can play an active role in making this topic easier:

Use Daily Life Examples: Shopping, pocket money, or home projects are great ways to explain percentages and ratios.
Encourage Verbal Explanation: Ask your child to explain how they solved a problem—it strengthens conceptual clarity.
Start Small and Build Up: Begin with simple examples before moving to complex word problems.
Use Visual Aids: Charts, tables, or diagrams make percentages, increases, and decreases easier to understand.
Practice Together: Solve problems as a team to make learning interactive and fun.

These tips create a supportive learning environment and build confidence in maths.

How to Check Answers and Avoid Common Errors

Even simple formulas can lead to mistakes if children don’t verify their work. Here’s how to help them:

Double-Check Values: Make sure the correct base and comparison values are used in the formula.
Estimate First: Roughly estimate the answer before calculating to see if it makes sense.
Step-by-Step Calculation: Avoid skipping steps, especially in percentage or profit/loss problems.
Cross-Check Using Reverse Calculation: For example, if calculating a 20% increase, subtract 20% from the final value to see if it matches the original.
Encourage Neat Work: Writing calculations clearly reduces errors and confusion.

By teaching children to check answers systematically, they develop accuracy and confidence in solving comparing quantities problems.

How PlanetSpark Helps Children Master Comparing Quantities

PlanetSpark uses a concept-based approach to help children truly understand comparing quantities instead of memorising formulas blindly.

Concept-First Teaching: Children learn why formulas work before applying them, making topics like percentages, profit, loss, and simple interest easier to grasp.
Step-by-Step Problem Solving: Each concept is broken down into clear steps, helping students identify base values, choose the right formula, and avoid common mistakes.
Real-Life Maths Examples: Lessons are linked to everyday situations such as shopping discounts, savings, pocket money, and exam scores, making maths practical and relatable.
Personalised One-to-One Guidance: Individual attention ensures children learn at their own pace and clear doubts instantly, building confidence and accuracy.
Confidence and Clarity Building: Regular practice with guided feedback helps children approach word problems calmly and score better in exams.

Conclusion

Comparing quantities becomes simple when children understand the underlying concepts instead of just memorising formulas. With clarity on percentages, profit, loss, ratios, and simple interest, children can solve problems confidently and accurately. Concept-based learning not only helps in exams but also develops real-life decision-making skills, from budgeting to understanding discounts.

Guided practice, real-life examples, and consistent problem-solving make maths engaging and enjoyable. Starting early ensures children build a strong foundation that supports higher-level maths and logical thinking.

Frequently Asked Questions

Comparing quantities means looking at two or more values to see how they relate, often using percentages, ratios, or differences.