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A shopkeeper marks his goods 25% above the cost price and allows a discount of 10%. What is his profit percentage?
12.5%
15%
10%
17.5%
12.5%
Use the net percentage change formula (successive percentage) for profit and discount: 25тИТ10+10025├Ч(тИТ10)тАЛ=15тИТ2.5=12.5%.
Marked price is 25% above the cost price, and a discount of 10% is allowed on the marked price.
Net%Change=x+y+100x├ЧyтАЛ
Use the net percentage change formula (successive percentage) for profit and discount: 25тИТ10+10025├Ч(тИТ10)тАЛ=15тИТ2.5=12.5%.
Students often subtract the discount percentage directly from the markup percentage (i.e., 25%тИТ10%=15%) instead of calculating the discount on the marked price.
Assume Cost Price
Let the cost price of the goods be 100.
CP=100
Calculate Marked Price
Since the goods are marked 25% above the cost price, the marked price becomes 125.
MP=100+25=125
Calculate Selling Price after Discount
A discount of 10% is allowed on the marked price (125), so the selling price is calculated as 125тИТ10%┬аof┬а125.
SP=125тИТ(0.10├Ч125)=125тИТ12.5=112.5
Determine Profit Percentage
The profit is the difference between the selling price (112.5) and the cost price (100), which gives a profit percentage of 12.5%.
Profit%=100112.5тИТ100тАЛ├Ч100=12.5%
A is correct because the calculated net profit percentage after a 25% markup and 10% discount is 12.5%.
This concept of successive percentage change is also widely applicable in compound interest, population growth, and mensuration scaling problems.
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