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A quantity is first decreased by 20% and then again decreased by 10%. What is the overall percentage decrease?
25%
28%
30%
32%
28%
Assume the initial value is 100. Decrease it by 20% to get 80, then decrease 80 by 10% (which is 8) to get 72. The difference from 100 is 28%.
A quantity undergoes a successive decrease of 20% followed by a decrease of 10%.
Net┬аChange=тИТaтИТb+100a├ЧbтАЛ
Assume the initial value is 100. Decrease it by 20% to get 80, then decrease 80 by 10% (which is 8) to get 72. The difference from 100 is 28%.
Most students add the percentages linearly (20% + 10% = 30%) and choose option C, ignoring the fact that the second decrease is applied to a reduced base.
Define the formula
To calculate the total percentage change for successive changes of a% and b%, use the formula for net percentage change.
Net┬аChange=тИТaтИТb+100a├ЧbтАЛ
Substitute the values
Here, both changes are decreases, so a=20 and b=10. Substituting these values into the expression:
Net┬аChange=тИТ20тИТ10+10020├Ч10тАЛ
Calculate the result
Performing the arithmetic: тИТ30+100200тАЛ=тИТ30+2=тИТ28. The negative sign indicates a decrease.
Net┬аChange=тИТ28%
B is correct because the successive application of a 20% decrease and a 10% decrease results in a total reduction of 28%.
This concept is identical to successive discounts in profit and loss or compound interest over two time periods.