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Two successive discounts of 10% and 5% are equivalent to a single discount of ______.
15.5%
14%
14.5%
15%
14.5%
Use the net percentage formula x+y−100xy directly for two successive discounts. Here 10+5−10010×5=15−0.5=14.5%.
Two successive discounts of 10% and 5%.
Dequivalent=x+y−100x×y
Use the net percentage formula x+y−100xy directly for two successive discounts. Here 10+5−10010×5=15−0.5=14.5%.
Many students mistakenly add the two percentages directly (10%+5%=15%) without accounting for the compounding effect on the reduced price.
Identify Given Discounts
We are given two successive discounts: x=10% and y=5%.
x=10%,y=5%
Apply Successive Discount Formula
The formula for the equivalent single discount of two successive percentage discounts x and y is given by: Dnet=x+y−100x×y
Dnet=x+y−100x×y
Substitute Values and Calculate
Substitute x=10 and y=5 into the formula: 10+5−10010×5=15−10050=15−0.5=14.5%
15 - 0.5 = 14.5\
C is correct because applying the successive discount formula 10+5−10010×5 yields a net single discount of 14.5%.
This same formula is used in compound percentage increase/decrease problems such as successive population growth or successive profit/loss percentages.
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