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Two successive discounts of 40% and 60% on a deal are equal to which single discount?
70%
66%
76%
80%
76%
Use the net percentage change formula x+y−100xy directly for successive discounts.
Two successive percentage discounts on a deal: d1=40% and d2=60%.
Dequivalent=(d1+d2−100d1×d2)%
Use the net percentage change formula x+y−100xy directly for successive discounts.
Many students incorrectly add the two discounts together (40%+60%=100%), forgetting that the second discount applies to the reduced price.
Step 1: Understand the formula for successive discounts
When two successive discounts of d1% and d2% are applied, the equivalent single discount percentage is given by the formula D=(d1+d2−100d1×d2)%
D=(d1+d2−100d1×d2)%
Step 2: Substitute the given values into the formula
Here, d1=40 and d2=60. Substituting these values into the formula: D=(40+60−10040×60)%
D=(40+60−1002400)%
Step 3: Simplify and calculate the final percentage
Simplify the expression inside the parentheses: D=100−24=76%
D = 76\
C is correct because two successive discounts of 40% and 60% are equivalent to a single discount of 76%.
This formula is identical to the net percentage change formula used in successive percentage increases/decreases (population growth, successive taxation).
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