Mastering Percentage Calculations
Percentages are everywhere - discounts, taxes, tips, grades. Learn the three main types of percentage problems and solve them instantly.
Three Types of Percentage Problems
Nearly every percentage question you encounter falls into one of three categories. Master these, and you can solve any percentage problem.
Type 1: What is X% of Y?
Formula: Result = (X / 100) × Y
Example: What is 15% of 200? (15 / 100) × 200 = 30
This is the most common type. You use it for calculating tips, discounts, and taxes. A 20% tip on a $45 meal is (20/100) × 45 = $9.00.
Type 2: X is what percent of Y?
Formula: Percentage = (X / Y) × 100
Example: 45 is what percent of 180? (45 / 180) × 100 = 25%
Use this when comparing parts to a whole. If you scored 38 out of 50 on a test: (38 / 50) × 100 = 76%.
Type 3: X is Y% of what number?
Formula: Whole = X / (Y / 100)
Example: 36 is 60% of what? 36 / (60 / 100) = 36 / 0.6 = 60
This type appears when you know the part and the percentage but need the original amount. If a discounted price of $68 represents 80% of the original price: 68 / 0.80 = $85 was the original.
Percentage Change
To find how much something increased or decreased:
% Change = [(New - Old) / Old] × 100
If a stock went from $40 to $52: [(52 - 40) / 40] × 100 = 30% increase.
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