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Two successive discounts of 12% and 15% on any number of toys bought are equivalent to a single discount of:
27%
26%
26.2%
25.2%
25.2%
Use the formula x+yтИТxy/100. Here 12+15=27 and 12├Ч15=180, so 180/100=1.8. Finally, 27тИТ1.8=25.2%.
Two successive discounts of 12% and 15% are applied to a product.
Single┬аDiscount=(x+yтИТ100x├ЧyтАЛ)%
Use the formula x+yтИТxy/100. Here 12+15=27 and 12├Ч15=180, so 180/100=1.8. Finally, 27тИТ1.8=25.2%.
Most students add the percentages directly (12% + 15% = 27%), forgetting that the second discount applies to the remaining balance after the first discount.
Define the discounts
Let the first discount be x=12% and the second discount be y=15%.
x=12,y=15
Apply the successive discount formula
To find the equivalent single discount, use the formula D=(x+yтИТ100xyтАЛ)%.
D=(12+15тИТ10012├Ч15тАЛ)%
Calculate the final percentage
Perform the arithmetic: 12+15=27 and 100180тАЛ=1.8. Subtracting gives 27тИТ1.8=25.2.
D=(27тИТ1.8)%=25.2%
D is correct because the equivalent discount of two successive discounts of 12% and 15% calculates to 25.2%.
This concept of successive percentage change is identical to calculating compound interest over two years or population growth rates.
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