Comparing Quantities: Percentages and Interest: Class 8 Study Guide
Percentages compare quantities out of 100. Interest is money paid for using money.
A percentage is a fraction out of 100. 25% = 25/100 = 1/4. To find x% of a number, multiply by x/100: 15% of ₹800 = ₹120. Profit and loss are measured against the cost price: Profit % = (profit ÷ cost price) × 100.
A discount is a reduction on the marked price. A ₹1,200 jacket with 20% off costs 1,200 − 240 = ₹960.
Simple and compound interest
Simple interest is charged on the original amount only: SI = P × R × T ÷ 100. For ₹10,000 at 10% a year for 2 years, SI = 10,000 × 10 × 2 ÷ 100 = ₹2,000. Compound interest is charged on the amount plus earlier interest: A = P(1 + R/100)ⁿ. For the same sum, A = 10,000 × 1.1 × 1.1 = ₹12,100, so CI = ₹2,100.
| Year | Simple interest | Compound interest |
|---|---|---|
| Start | ₹10,000 | ₹10,000 |
| After year 1 | ₹11,000 | ₹11,000 |
| After year 2 | ₹12,000 | ₹12,100 |
Steps
Read the problem and identify P (principal), R (rate per year) and T or n (years). Choose simple or compound interest. Calculate, then write the amount or interest, as asked, with the unit ₹.
From the problem.
Simple or compound.
Year by year if n is small.
Is the answer reasonable?
Real-life uses
Banks pay interest on savings and charge interest on loans. A GST or sales tax is a percentage of the price, and a discount sale can be compared using percentages. Understanding interest helps us avoid unnecessary debt.
Worked examples and common mistakes
Example: A shirt costs ₹500 and is sold for ₹600. Profit % = 100 ÷ 500 × 100 = 20%. Example: SI on ₹5,000 at 8% for 3 years = ₹1,200. Common mistakes: finding profit % on the selling price, and using the compound formula for simple interest. Name each step.
Check your understanding: model answers
1. ₹300. 2. 4,000 × 5 × 3 ÷ 100 = ₹600. 3. 1,000 × 1.1 × 1.1 = ₹1,210.
✨ Key Takeaways
- Percent means out of 100.
- Profit % is profit ÷ cost price × 100.
- SI = PRT ÷ 100.
- Compound interest is charged on interest too.
💬 Questions for Discussion & Reflection
- Find 12% of ₹2,500.
- Find the SI on ₹4,000 at 5% for 3 years.
- Find the compound amount on ₹1,000 at 10% for 2 years.