Percentage Change

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Calculate the result after increasing or decreasing a value by a percentage.

Percentage change problems involve applying an increase or decrease to a starting value. For an increase of X%, multiply by (1 + X/100). For a decrease of X%, multiply by (1 - X/100). This is more direct than reverse percentage since you're moving forward from the original to the final value.

Increase: Final = Original × (1 + X/100). Decrease: Final = Original × (1 - X/100)

• 100 increased by 20% = 100 × 1.20 = 120
• 80 decreased by 25% = 80 × 0.75 = 60
• 150 increased by 10% = 150 × 1.10 = 165

How to recognize it

• Given a starting value and a percentage change
• Asked for the new/final value
• Keywords: 'increases by', 'decreases by', 'goes up', 'goes down'

Common mistakes

• Adding/subtracting the percentage instead of using a multiplier
• Confusing 'increased by 20%' with 'increased to 120%'
• Using the wrong direction (1.20 for increase, 0.80 for 20% decrease)

Practice guidance

Numerical Reasoning