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A dishonest trader marks his goods 20% above cost price and allows a discount of 10%. What is his net profit percentage?
8%
10%
12%
6%
8%
Use the net percentage change formula x+y+(xy/100). Here, x=+20 and y=тИТ10. So, 20тИТ10+(20├ЧтИТ10)/100=10тИТ2=8.
Marked price is 20% above Cost Price (CP), and a discount of 10% is offered on the marked price.
Net%=x+y+100x├ЧyтАЛ
Use the net percentage change formula x+y+(xy/100). Here, x=+20 and y=тИТ10. So, 20тИТ10+(20├ЧтИТ10)/100=10тИТ2=8.
Many students incorrectly subtract the discount from the markup percentage (20тИТ10=10%) without considering that the discount is applied to the already marked-up price.
Assume Cost Price
Let the Cost Price (CP) be 100.
CP=100
Calculate Marked Price
Since the goods are marked 20% above cost, the Marked Price (MP) becomes 100+20%┬аof┬а100.
MP=100├Ч1.20=120
Apply Discount
A discount of 10% is applied to the Marked Price of 120. Selling Price (SP) = 120тИТ10%┬аof┬а120.
SP=120тИТ12=108
Calculate Net Profit
The profit is the difference between Selling Price (108) and Cost Price (100).
Profit%=100108тИТ100тАЛ├Ч100=8%
A is correct because the net effect of a 20% increase followed by a 10% decrease results in a final profit of 8%.
This successive percentage formula is identical to the one used for calculating compound interest for two years or successive discounts in consumer math.
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