📘 Percentage

🔹 What is Percentage?

Percentage means “per hundred”. It is used to compare quantities with 100 as the base.

\[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \]

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📐 Basic Percentage Formulas

\[ x\% = \frac{x}{100} \]

\[ x\% \text{ of } y = \frac{x}{100} \times y \]

\[ \text{Value} = \frac{\text{Percentage} \times \text{Total}}{100} \]

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🧠 Exam Shortcuts & Tricks

Shortcut 1:
10% = divide by 10
20% = divide by 5
25% = divide by 4
50% = divide by 2

Shortcut 2:
Increase by x% ⇒ multiply by \(1 + \frac{x}{100}\)
Decrease by x% ⇒ multiply by \(1 - \frac{x}{100}\)

Shortcut 3:
If A is x% more than B, then B is \[ \frac{x}{100+x} \times 100 \% \text{ less than A} \]

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✍️ Solved Examples

Example 1:
Find 20% of 150. \[ 20\% \text{ of } 150 = \frac{20}{100} \times 150 = 30 \]

Example 2:
What percent of 50 is 10? \[ \text{Percentage} = \frac{10}{50} \times 100 = 20\% \]

Example 3:
A number is increased by 10%. Find the multiplying factor. \[ 1 + \frac{10}{100} = 1.1 \]

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📊 Percentage Increase & Decrease

\[ \text{Increase %} = \frac{\text{Increase}}{\text{Original Value}} \times 100 \]

\[ \text{Decrease %} = \frac{\text{Decrease}}{\text{Original Value}} \times 100 \]

Example:
Price of an item increases from ₹100 to ₹120. \[ \text{Increase \%} = \frac{20}{100} \times 100 = 20% \]

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