📊 Percentages

Learn the concept, formulas, shortcuts and problem-solving techniques for percentages.

📖 1. Concept

Percentage means "per hundred".

The symbol used for percentage is %.

20% = 20 / 100 = 1 / 5

Therefore:

20% of 500 = (20 / 100) × 500 = 100

📌 2. Important Formulas

Percentage = (Part / Whole) × 100
Part = (Percentage / 100) × Whole
Percentage Increase = (Increase / Original Value) × 100
Percentage Decrease = (Decrease / Original Value) × 100

🧮 3. Solved Examples

Example 1

Find 20% of 500.

20% of 500 = (20 / 100) × 500 = 100

✅ Answer: 100

Example 2

A student scored 72 marks out of 90. Find the percentage.

Percentage = (72 / 90) × 100 = 80%

✅ Answer: 80%

Example 3

A number increases from 200 to 240. Find the percentage increase.

Increase = 240 - 200 = 40

Percentage Increase = (40 / 200) × 100 = 20%

✅ Answer: 20%

⚡ 4. Shortcuts

10% → Divide the number by 10.
5% → Find 10% and divide by 2.
25% → Divide the number by 4.
50% → Divide the number by 2.

⚠️ 5. Common Mistakes

Mistake 1: Using the new value instead of the original value when calculating percentage increase or decrease.
Mistake 2: Forgetting to multiply by 100 when calculating percentage.

✍️ 6. Practice Problems

1. Find 25% of 800.
25% of 800 = (25 / 100) × 800 = 200
2. Find 15% of 600.
15% of 600 = (15 / 100) × 600 = 90
3. A number increases from 400 to 500. Find the percentage increase.
Increase = 500 - 400 = 100

Percentage increase = (100 / 400) × 100 = 25%
4. A price decreases from ₹800 to ₹680. Find the percentage decrease.
Decrease = 800 - 680 = 120

Percentage decrease = (120 / 800) × 100 = 15%
5. 30 is what percentage of 150?
Percentage = (30 / 150) × 100 = 20%