Understanding how to calculate percentage increases and decreases is vital for interpreting data changes in real-world scenarios and GMAT problems.
Percentage Increase measures how much a quantity has grown relative to its original value.
Formula: Percentage Increase = [(New Value - Original Value) / Original Value] × 100%
Example: A product's price increases from $50 to $65. What is the percentage increase?
Solution:Percentage Increase = [(65 - 50) / 50] × 100% = (15 / 50) × 100% = 30%
Percentage Decrease measures how much a quantity has reduced relative to its original value.
Formula:Percentage Decrease = [(Original Value - New Value) / Original Value] × 100%
Example: A laptop's price decreases from $800 to $640. What is the percentage decrease?
Solution: Percentage Decrease = [(800 - 640) / 800] × 100% = (160 / 800) × 100% = 20%
When multiple percentage changes occur sequentially, it's essential to apply each change to the new value after the previous change.
Example: A shirt's price is increased by 10% in the first year and then decreased by 10% in the second year. What is the net percentage change?
Solution:
Initial Price = $100 (Assume for simplicity)
After 10% Increase: $100 + (10% × $100) = $100 + $10 = $110
After 10% Decrease: $110 - (10% × $110) = $110 - $11 = $99
Net Change: $99 - $100 = -$1 → 1% decrease
Note: The net percentage change is not simply the sum or difference of the individual percentages due to the base value changing after each operation.