Comparing Quantities Class 8 Full Practice | PlanetSpark

Mathematics becomes more interesting when we connect it to real life. One such practical chapter in middle school maths is Comparing quantities. From shopping discounts to bank interest and profit calculations, this topic is everywhere around us. If you are studying comparing quantities of class 8, this detailed guide will help you understand concepts, formulas, and practice questions in a clear and simple way.

In this blog, we will cover:

• Meaning of comparing quantities
• Important concepts and formulas
• Comparing quantities all formulas in one place
• Profit and loss
• Discount
• Simple interest
• Compound interest
• Increase and decrease percentage
• Practice questions with solutions

Let us begin step by step.

What Is Comparing Quantities

Comparing quantities means finding how much one quantity is more or less than another. It is usually done using ratios and percentages.

For example:

• If a shirt costs 500 and you get it for 450, how much discount did you get
• If you buy something for 200 and sell it for 250, what is your profit
• If a bank gives 5 percent interest, how much extra money will you earn

All these situations involve comparing two amounts.

In comparing quantities of class 8, students learn how to convert fractions into percentages, calculate increase and decrease, and apply formulas in daily life problems.

Basic Concepts of Comparing Quantities

Before jumping into formulas, let us understand the base ideas.

1. Ratio

A ratio compares two quantities.

Example
If there are 20 boys and 25 girls in a class
Ratio of boys to girls = 20 : 25 = 4 : 5

2. Percentage

Percentage means per hundred.

If 40 students out of 100 passed, pass percentage = 40 percent.

To convert:

• Fraction to percentage multiply by 100
• Decimal to percentage multiply by 100
• Percentage to fraction divide by 100

Example
0.25 into 100 = 25 percent

Increase and Decrease Percentage

In daily life, prices increase and decrease. Understanding percentage change is very important in Comparing quantities.

Percentage Increase Formula

Percentage increase = Increase divided by Original value into 100

Example
Price of a bag increases from 1000 to 1200

Increase = 200
Percentage increase = 200 divided by 1000 into 100 = 20 percent

Percentage Decrease Formula

Percentage decrease = Decrease divided by Original value into 100

Example
Price drops from 800 to 600

Decrease = 200
Percentage decrease = 200 divided by 800 into 100 = 25 percent

These calculations are common in percentage increase and decrease problems.

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Profit and Loss

One of the most important parts of comparing quantities of class 8 is profit and loss.

Important Terms

• Cost Price CP
• Selling Price SP
• Profit
• Loss

If SP is greater than CP, there is profit.
If CP is greater than SP, there is loss.

Profit Formula

Profit = SP minus CP

Profit percent = Profit divided by CP into 100

Loss Formula

Loss = CP minus SP

Loss percent = Loss divided by CP into 100

Example 1 Profit

A shopkeeper buys a book for 200 and sells it for 250.

Profit = 250 minus 200 = 50
Profit percent = 50 divided by 200 into 100 = 25 percent

Example 2 Loss

A pen is bought for 100 and sold for 80.

Loss = 100 minus 80 = 20
Loss percent = 20 divided by 100 into 100 = 20 percent

Understanding profit and loss class 8 questions is essential for exams and real life.

Discount

Whenever you visit a mall and see 30 percent off, that is discount.

Marked Price MP is the price written on the tag.
Selling Price SP is the price after discount.

Discount Formula

Discount = Marked Price minus Selling Price

Discount percent = Discount divided by Marked Price into 100

Example

Marked price of a jacket is 1000.
Discount given is 20 percent.

Discount amount = 20 percent of 1000 = 200
Selling price = 1000 minus 200 = 800

Discount problems are very common in comparing quantities all formulas practice.

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Simple Interest

Banks and money lending involve interest.

Principal P is the money borrowed.
Rate R is the interest rate per year.
Time T is the duration.

Simple Interest Formula

Simple Interest SI = P into R into T divided by 100

Amount = P plus SI

Example

Principal = 5000
Rate = 10 percent
Time = 2 years

SI = 5000 into 10 into 2 divided by 100 = 1000

Amount = 5000 plus 1000 = 6000

This concept is a major part of simple interest and compound interest class 8.

Compound Interest

Compound interest is calculated on principal plus previous interest.

Formula for Compound Interest

Amount = P into 1 plus R divided by 100 whole power T

Compound Interest = Amount minus Principal

Example

Principal = 10000
Rate = 10 percent
Time = 2 years

Amount = 10000 into 1.10 whole power 2
= 10000 into 1.21
= 12100

Compound Interest = 12100 minus 10000 = 2100

Compound interest grows faster than simple interest. That is why banks and investments use it.

Finding GST and Tax

In modern problems of Comparing quantities, GST is also included.

GST Formula

GST amount = Rate percent of original price

Final price = Original price plus GST

Example
Price of phone = 20000
GST = 18 percent

GST amount = 18 percent of 20000 = 3600
Final price = 23600

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Comparing Ratios with Percentages

Sometimes questions combine ratio and percentage.

Example
Income of A and B is in ratio 3 : 2.
If total income is 50000, find individual income.

Total parts = 5
One part = 50000 divided by 5 = 10000

A income = 3 into 10000 = 30000
B income = 2 into 10000 = 20000

Comparing Quantities All Formulas Quick Revision

Here are comparing quantities all formulas in one place:

• Percentage = Value divided by Total into 100
• Increase percent = Increase divided by Original into 100
• Decrease percent = Decrease divided by Original into 100
• Profit = SP minus CP
• Profit percent = Profit divided by CP into 100
• Loss = CP minus SP
• Loss percent = Loss divided by CP into 100
• Discount = MP minus SP
• Discount percent = Discount divided by MP into 100
• Simple Interest = P into R into T divided by 100
• Amount in SI = P plus SI
• Compound Amount = P into 1 plus R divided by 100 whole power T
• Compound Interest = Amount minus P

Keep this list handy for revision.

Practice Questions

Let us solve mixed practice from comparing quantities of class 8.

Question 1

A bicycle was bought for 4000 and sold at 10 percent profit. Find SP.

Profit = 10 percent of 4000 = 400
SP = 4000 plus 400 = 4400

Question 2

The price of a shirt decreases from 1500 to 1200. Find percentage decrease.

Decrease = 300
Percentage decrease = 300 divided by 1500 into 100 = 20 percent

Question 3

Find SI on 8000 at 5 percent for 3 years.

SI = 8000 into 5 into 3 divided by 100
= 1200

Question 4

Marked price of shoes is 2000. Discount is 25 percent. Find SP.

Discount = 25 percent of 2000 = 500
SP = 1500

Word Problems for Strong Practice

Problem 1

A trader bought 50 pens at 10 each. He sold each pen at 12. Find total profit percent.

Total CP = 50 into 10 = 500
Total SP = 50 into 12 = 600

Profit = 100
Profit percent = 100 divided by 500 into 100 = 20 percent

Problem 2

Population of a town increased from 20000 to 25000. Find percentage increase.

Increase = 5000
Percentage increase = 5000 divided by 20000 into 100 = 25 percent

Common Mistakes Students Make

While learning Comparing quantities, students often:

• Forget to divide by original value in percentage
• Confuse CP and MP
• Use wrong formula for compound interest
• Forget to convert percentage into fraction

Avoid these mistakes by practicing regularly.

Why Comparing Quantities Is Important

This chapter builds strong foundation for higher classes. Concepts of:

• Business maths
• Banking
• Investment
• Economics

are based on percentage and comparison.

Understanding comparing quantities of class 8 clearly will help in future competitive exams as well.

Tips to Score Full Marks

• Learn all formulas by heart
• Practice mixed word problems
• Revise comparing quantities all formulas weekly
• Focus on units and percentage conversion
• Solve previous year question papers

Why Choose PlanetSpark for Comparing Quantities Practice

• Live interactive classes that simplify Comparing quantities with real life examples and step by step explanations

• Dedicated mentors who focus on clearing doubts in topics like profit and loss class 8, discount, and interest

• Structured worksheets covering comparing quantities of class 8 with gradual difficulty levels

• Complete revision support including comparing quantities all formulas and shortcut techniques

• Regular assessments and performance tracking to improve accuracy and speed

• Personalized attention to help students build confidence in percentage and application based word problems

• A supportive learning environment that makes maths engaging, practical, and easy to understand

Conclusion

Comparing quantities is not just a school chapter. It is a life skill. From calculating discounts during shopping to understanding interest in banks, this topic helps in smart financial decisions.

If you practice regularly and understand each formula clearly, you will find this chapter easy and scoring. Keep revising comparing quantities all formulas, solve different types of questions, and build confidence step by step.

Mathematics becomes simple when concepts are clear. So keep practicing and enjoy learning with PlanetSpark.