Compound Percentage

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Calculate the result of applying multiple percentage changes in sequence.

Compound percentage problems involve applying multiple percentage changes one after another. Each change is applied to the result of the previous change, not the original value. A 10% increase followed by a 10% increase is NOT a 20% total increase—it's 1.10 × 1.10 = 1.21, or 21%.

After changes of X% then Y%: Final = Original × (1 + X/100) × (1 + Y/100)

• 100 increased by 10% then 20%: 100 × 1.10 × 1.20 = 132 (not 130)
• 200 up 25% then down 20%: 200 × 1.25 × 0.80 = 200 (back to start)
• Price up 50% then down 50%: Not zero! 100 × 1.50 × 0.50 = 75

How to recognize it

• Multiple percentage changes applied in sequence
• Each change applies to the result of the previous
• Keywords: 'then', 'followed by', 'successive'

Common mistakes

• Adding percentages together (10% + 20% = 30%, wrong!)
• Thinking opposite changes cancel out (up 50%, down 50% ≠ original)
• Applying both percentages to the original value

Practice guidance

Numerical Reasoning