Summary
Chapter 7 of Class 8 maths (Mathematics Old), '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.
This chapter builds on ratio and percentage concepts, then applies them to real-world financial scenarios. Students learn to find discounts from marked prices, calculate taxes added to bills, and work with compound interest—where interest is calculated on the previous year's total amount rather than just the original principal. Key formulas and year-by-year calculations show why compound interest grows faster than simple interest.
Key points & formulas
- 01Ratio compares two quantities (e.g., apples to oranges); it can be simplified using fractions or percentages
- 02Discount = Marked Price − Sale Price; discount percent is always calculated on the marked price
- 03Sales tax (ST), Value Added Tax (VAT), and Goods and Services Tax (GST) are added to the bill amount by the government
- 04Compound Interest is calculated on the previous year's total amount (Principal + Interest), not just the original principal
- 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
- 06Compound interest applies to population growth, bacterial growth, and depreciation (decrease in value over time)
- 07Simple Interest over 2 years at 10% on ₹100 yields ₹120; Compound Interest yields ₹121—the difference grows with more years
Frequently asked questions
01What is Comparing Quantities about?
It teaches how to compare quantities using ratios (e.g., 3:2) and percentages, then applies these skills to practical situations like shopping discounts, taxes on bills, and earning interest on money in banks.
02How do I calculate a discount?
First find the discount amount: Discount = Marked Price − Sale Price. Then find the discount percentage: Discount% = (Discount ÷ Marked Price) × 100. For example, an item marked ₹840 sold for ₹714 has a discount of ₹126, which is 15% of the marked price.
03What is the difference between Simple Interest and Compound Interest?
In Simple Interest, interest is calculated only on the original principal every year. In Compound Interest, interest is added to the principal each year, and next year's interest is calculated on the new total. Over time, Compound Interest becomes significantly larger.
04What is the compound interest formula?
The formula is A = P(1 + R/100)ⁿ, where A is the final amount, P is the principal, R is the interest rate per annum, and n is the number of years. To find Compound Interest: CI = A − P.
05Is the Class 8 maths Comparing Quantities chapter PDF free to download?
Yes, NCERT textbook PDFs including this chapter are free to download, with no sign-up required.
More chapters in Mathematics
This is the complete Mathematics Chapter 7 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 8 textbooks.
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