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A shopkeeper marks his goods 40% above the cost price and allows a discount of 15%. What is his profit percentage?
19%
25%
21%
15%
19%
Use the net percentage change formula (successive percentage formula) where mark-up is positive and discount is negative: 40тИТ15тИТ10040├Ч15тАЛ.
Marked price is 40% above the cost price, and the discount allowed is 15%.
\text{Net Profit %} = \left( x + y + \frac{xy}{100} \right)
Use the net percentage change formula (successive percentage formula) where mark-up is positive and discount is negative: 40тИТ15тИТ10040├Ч15тАЛ.
Students often mistakenly subtract the discount directly from the mark-up (40%тИТ15%=25%) without accounting for the fact that the discount is applied on the marked price, not the cost price.
Assume Cost Price
Let the cost price of the goods be 100.
Cost┬аPrice┬а(CP)=100
Calculate Marked Price
Since the goods are marked 40% above the cost price, the marked price becomes 140.
Marked┬аPrice┬а(MP)=100+10040тАЛ├Ч100=140
Calculate Selling Price after Discount
A discount of 15% is allowed on the marked price of 140, giving the selling price.
Selling┬аPrice┬а(SP)=140тИТ10015тАЛ├Ч140=140тИТ21=119
Determine Profit Percentage
With a cost price of 100 and a selling price of 119, the net profit percentage is 19%.
\text{Profit %} = \frac{119 - 100}{100} \times 100 = 19\%
A is correct because the calculated profit percentage is 19%.
This successive percentage concept is identical to compound percentage change formulas used in population growth and simple/compound interest problems.
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