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If the price of an item increases by 20% and then decreases by 20%, what is the net percentage change in the price?
0% increase
4% decrease
4% increase
2% decrease
4% decrease
Use the formula 100x2тАЛ for successive percentage increase and decrease of the same value x. The result is always a decrease.
Initial price change = +20%, Subsequent price change = -20%.
Net%Change=x+y+100x├ЧyтАЛ
Use the formula 100x2тАЛ for successive percentage increase and decrease of the same value x. The result is always a decrease.
Students often assume the net change is 0% by cancelling out +20% and -20%, failing to realize the second percentage applies to the new adjusted price, not the original.
Define variables
Assign x=20 for the increase and y=тИТ20 for the decrease.
x=20,y=тИТ20
Apply Successive Percentage Formula
Substitute the values into the standard successive percentage formula.
Net%=20+(тИТ20)+10020├Ч(тИТ20)тАЛ
Calculate the result
Solve the arithmetic expression to find the final percentage change.
Net%=0тИТ100400тАЛ=тИТ4%
B is correct because the calculated net percentage change is -4%, which signifies a 4% decrease.
This concept is essential for Compound Interest problems where interest is applied on a changing principal amount over successive periods.
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