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A quantity is first decreased by 12% and then again decreased by 8%. What is the overall percentage decrease?
21.04%
18.96%
19.04%
20.96%
19.04%
Use the effective percentage formula: тИТ(a+b)+100a├ЧbтАЛ. For 12% and 8%, it becomes тИТ(12+8)+10012├Ч8тАЛ=тИТ20+0.96=тИТ19.04%.
A quantity undergoes two successive decreases: first by 12% and then by 8%.
Net┬аPercentage┬аChange=тИТaтИТb+100a├ЧbтАЛ
Use the effective percentage formula: тИТ(a+b)+100a├ЧbтАЛ. For 12% and 8%, it becomes тИТ(12+8)+10012├Ч8тАЛ=тИТ20+0.96=тИТ19.04%.
Most students simply add the percentages to get 20%, forgetting that the second decrease applies to the remaining value, not the original value.
Define variables
Let the two successive percentage decreases be a=12 and b=8.
a=12,b=8
Apply Successive Percentage Formula
The formula for two successive decreases is тИТ(a+b)+100a├ЧbтАЛ.
Total┬аChange=тИТ(12+8)+10012├Ч8тАЛ
Calculate the result
Calculate the sum of the decreases and the adjustment term: тИТ20+10096тАЛ=тИТ20+0.96.
тИТ20+0.96=тИТ19.04
C is correct because the successive application of a 12% decrease and an 8% decrease results in an overall reduction of 19.04%.
This concept is identical to calculating successive discounts in profit and loss or compound interest (where the rate is negative for depreciation).
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