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A retailer permits a trade discount of 25%, followed by a cash discount of 8%, on an article. The net percentage of discount is:
33%
34%
32%
31%
31%
Use the formula Dnet=(d1+d2)−100d1d2. Here, 25+8−10025×8=33−2=31%.
Trade discount d1 = 25%, cash discount d2 = 8%.
Net Discount=d1+d2−100d1×d2
Use the formula Dnet=(d1+d2)−100d1d2. Here, 25+8−10025×8=33−2=31%.
Adding the percentages directly (25% + 8% = 33%) is incorrect as the second discount is applied to the reduced price, not the original price.
Identify given discounts
The retailer offers two successive discounts. First discount d1=25% and second discount d2=8%.
d1=25%,d2=8%
Apply net discount formula
To find the equivalent single percentage discount, apply the formula for successive percentage changes.
Dnet=d1+d2−100d1×d2
Calculate the result
Substitute the values into the formula: 25+8−10025×8=33−100200=33−2=31%
Dnet=31%
D is correct because the net equivalent discount of 25% and 8% is 31%.
This concept of 'successive percentage change' is identical to the calculation used for compound interest compounding annually or successive tax increases/decreases.
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