Comparing Quantities
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- Percentage means per hundred.
- Profit = SP - CP; loss = CP - SP.
- Profit and loss percentages are based on cost price.
- Discount = marked price - selling price.
- Simple interest uses the original principal; compound interest adds interest to the amount.
What You Will Learn
- Convert between fractions, decimals and percentages
- Calculate percentage increase or decrease
- Solve profit and loss problems
- Solve discount problems
- Calculate simple and compound interest
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Percentage
A percentage is a fraction with denominator 100. Convert a fraction to percentage by multiplying by 100%. Convert a percentage to decimal by dividing by 100.
Profit and loss
Profit occurs when SP > CP; loss occurs when SP < CP. Percentage is measured against cost price.
Discount
Discount is the reduction from marked price. Discount percentage is measured against marked price.
Simple interest
Simple interest is calculated on the original principal throughout the time period.
Compound interest
Compound interest is calculated on the amount after previous interest has been added. For annual compounding, each year's amount becomes the next year's principal.
Formula Sheet
Formula / Key Relations
Percentage
Use the correct whole.
Profit percentage
Profit = SP - CP.
Loss percentage
Loss = CP - SP.
Discount percentage
Discount = MP - SP.
Simple interest
R per year, T in years.
Compound amount
For annual compounding.
Worked Examples
Profit percent is 15%.
Selling price is ₹880.
Exam Traps
Quick Revision
Quick Revision
- Percentage means per hundred.
- Profit = SP - CP; loss = CP - SP.
- Profit and loss percentages are based on cost price.
- Discount = marked price - selling price.
- Simple interest uses the original principal; compound interest adds interest to the amount.
- Revise the formula sheet once more before attempting questions.
Compact Practice
20% of 250?
View Solution
50
CP ₹500, SP ₹450. Loss percent?
View Solution
10%
MP ₹2000, discount 15%. SP?
View Solution
₹1700
Simple interest on ₹2000 at 5% p.a. for 3 years?
View Solution
₹300
Final Chapter Summary
Chapter Summary
- Percentage means per hundred.
- Profit = SP - CP; loss = CP - SP.
- Profit and loss percentages are based on cost price.
- Discount = marked price - selling price.
- Simple interest uses the original principal; compound interest adds interest to the amount.
- Prioritise correct method, clean working and final units where applicable.