Chapter 7 — Comparing Quantities

Chapter 7 of the Class 8 Maths NCERT textbook, 'Comparing Quantities', teaches how to compare quantities using ratios and percentages, and introduces applications like finding discounts, calculating sales tax (ST/VAT/GST), and understanding compound interest on borrowed or deposited money.

• Ratios and percentages in commerce — The chapter applies ratio and percentage skills to shopping and finance — computing discounts on marked prices and adding government taxes like ST, VAT and GST to bills.
• How compound interest grows — Compound interest charges each period's interest on the running total rather than the original principal, so it grows faster than simple interest — shown through year-by-year calculations and a compact formula.
• Growth beyond money — The same compounding idea models population and bacterial growth as well as depreciation, showing that percentage change over repeated periods explains many real-world increases and decreases.

1. 01Ratio compares two quantities (e.g., apples to oranges); it can be simplified using fractions or percentages
2. 02Discount = Marked Price − Sale Price; discount percent is always calculated on the marked price
3. 03Sales tax (ST), Value Added Tax (VAT), and Goods and Services Tax (GST) are added to the bill amount by the government
4. 04Compound Interest is calculated on the previous year's total amount (Principal + Interest), not just the original principal
5. 05Compound Interest formula: A = P(1 + R/100)ⁿ, where A is final amount, P is principal, R is rate per annum, and n is number of years
6. 06Compound interest applies to population growth, bacterial growth, and depreciation (decrease in value over time)
7. 07Simple Interest over 2 years at 10% on ₹100 yields ₹120; Compound Interest yields ₹121—the difference grows with more years