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Two successive discounts of 25% and 10% on a deal are equivalent to a single discount of:
32%
34.5%
32.5%
35%
32.5%
Use the net percentage change formula a+b−100ab where a=25 and b=10, giving 25+10−10025×10=35−2.5=32.5%.
Two successive discounts of 25% and 10% on a deal.
Dequivalent=(a+b−100a×b)%
Use the net percentage change formula a+b−100ab where a=25 and b=10, giving 25+10−10025×10=35−2.5=32.5%.
Many students mistakenly add the discounts directly (25%+10%=35%) without accounting for the successive compounding effect.
Step 1: Understand Successive Discounts
When two successive discounts a% and b% are applied, the net single equivalent discount is given by the formula:
Dequivalent=(a+b−100a×b)%
Step 2: Substitute the Given Values
Substitute a=25 and b=10 into the formula:
Dequivalent=(25+10−10025×10)%
Step 3: Calculate the Result
Simplify the expression inside the parentheses: 25+10=35 and 100250=2.5. Therefore, 35−2.5=32.5%.
Dequivalent=35−2.5=32.5%
C is correct because two successive discounts of 25% and 10% are equivalent to a single discount of 32.5%.
This formula is identical to the net population growth and successive profit/loss percentage formulas used in compound interest and percentage chapters.
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