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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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A shopkeeper provides successive discounts of 5% and 4%, which are equivalent to a single discount of ______.
9%
8%
9.2%
8.8%
8.8%
Use the net percentage change formula a+b−100ab for two successive percentage changes to get the answer instantly in 5 seconds.
Two successive discounts are 5% and 4%.
Equivalent Discount=(a+b−100a×b)%
Use the net percentage change formula a+b−100ab for two successive percentage changes to get the answer instantly in 5 seconds.
Students often just add the two percentages (5%+4%=9%) and forget to subtract the product over 100.
Step 1: Identify the Successive Discount Percentages
Let the first discount be a=5% and the second discount be b=4%.
a=5,b=4
Step 2: Apply the Successive Discount Formula
The formula for a single equivalent discount of two successive discounts a% and b% is given by: Equivalent Discount=(a+b−100a×b)%
Equivalent Discount=(5+4−1005×4)%
Step 3: Calculate the Final Value
Substitute the values into the formula and simplify: 5+4−10020=9−0.20=8.80%=8.8%
9−0.20=8.8%
D is correct because the equivalent single discount for successive discounts of 5% and 4% is 8.8%.
This formula is identical to the net percentage increase/decrease formula used in successive population growth or compound price changes.
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