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Two successive discounts of 30% and 35% on a deal are equivalent to a single discount of:
60%
65%
54.5%
55.5%
54.5%
Use the net percentage change formula a+b−100ab where a=30 and b=35.
Two successive discounts of 30% and 35% on a deal.
Dequivalent=a+b−100a×b
Use the net percentage change formula a+b−100ab where a=30 and b=35.
Many students simply add the two discounts (30%+35%=65%), forgetting that the second discount applies to the reduced price.
Step 1: Understand Successive Discounts
When two successive discounts of a% and b% are applied, the net percentage discount equivalent to a single discount is given by the formula:
Dequivalent=a+b−100a×b
Step 2: Substitute the Given Values
Substitute a=30 and b=35 into the formula:
Dequivalent=30+35−10030×35
Step 3: Calculate the Net Discount
Simplify the expression by performing the multiplication and addition:
Dequivalent=65−1001050=65−10.5=54.5%
C is correct because the equivalent single discount for two successive discounts of 30% and 35% is calculated as 30+35−10030×35=54.5%.
This formula is identical to the net percentage change formula used for successive percentage increases and decreases in profit/loss and population growth problems.
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