Common Percentage Problems

Percentages appear everywhere—discounts, tips, tax, test scores, and interest. Master the basics with these patterns.

Find X% of a Number

X% of N = (X / 100) × N

Example: 15% of 80 = 0.15 × 80 = 12

Percentage Change

% Change = (New − Old) / Old × 100%

Example: From 50 to 65 → (65 − 50) / 50 × 100% = 30%

Reverse Percentage

If 90 is after a 10% discount, original price is 90 / (1 − 0.10) = 100.

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When calculating discount plus tax, be mindful of order: a 20% discount followed by an 8% sales tax is not the same as applying them in the opposite order unless the tax base is defined by law. Similarly, a 20% decrease followed by a 20% increase does not return you to the original value; the net effect is a 4% decrease. These compounding effects are common sources of confusion in everyday math.