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If the marked price of the computer is 20% more than its cost price and the shopkeeper offers a discount of 15% on the marked price of the computer, then find the profit percentage of the computer.
5%
1%
3%
2%
None of the above
2%
Use the formula (1+x/100)(1тИТy/100)тИТ1 where x=20 is mark-up and y=15 is discount, resulting in (1.20├Ч0.85)тИТ1=1.02тИТ1=0.02, which is 2%.
Marked Price of Computer = тВ╣15,000; Marked Price is 20% more than Cost Price; Discount offered = 15% on Marked Price.
Profit┬а%=(Cost┬аPriceSelling┬аPriceтИТCost┬аPriceтАЛ)├Ч100
Use the formula (1+x/100)(1тИТy/100)тИТ1 where x=20 is mark-up and y=15 is discount, resulting in (1.20├Ч0.85)тИТ1=1.02тИТ1=0.02, which is 2%.
Students often calculate 15% discount on the Cost Price instead of the Marked Price, or mistakenly add/subtract percentages directly (i.e., 20 - 15 = 5).
Calculate Cost Price (CP)
Since MP is 20% more than CP, let CP=100 units. Then MP=120 units. Given MP=15000, we find CP=1.2015000тАЛ.
CP=12500
Calculate Selling Price (SP)
The shopkeeper offers a 15% discount on the MP of 15000. SP=MP├Ч(1тИТ0.15).
SP=15000├Ч0.85=12750
Calculate Profit Percentage
Profit = SPтИТCP=12750тИТ12500=250. Profit percentage = CPProfitтАЛ├Ч100.
12500250тАЛ├Ч100=2%
D is correct because the calculated profit percentage is exactly 2%.
This concept of effective percentage change is identical to calculating successive discounts or tax increases, often used in Compound Interest problems.
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