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Examoogle • User • info@examoogle.com • EE-2024-8821
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A shopkeeper fixes the marked price of an item 20% above its cost price. What percentage of discount should he offer to gain 2%?
15%
17%
12%
18%
15%
Use the formula: D% = ((MP% - P%) / (100 + MP%)) * 100. Here, ((120 - 102) / 120) * 100 = 18/120 * 100 = 15%.
Marked price is 20% above Cost Price (CP), and the target is to gain 2% profit.
D=MPMP−SP×100
Use the formula: D% = ((MP% - P%) / (100 + MP%)) * 100. Here, ((120 - 102) / 120) * 100 = 18/120 * 100 = 15%.
Many students subtract the profit percentage (2%) directly from the markup (20%), incorrectly arriving at 18%, which ignores that profit is calculated on CP while discount is on MP.
Assume Cost Price
Let the Cost Price (CP) be 100. Since the shopkeeper marks the price 20% above CP, the Marked Price (MP) is 120.
CP=100,MP=120
Calculate Selling Price
To gain a profit of 2%, the Selling Price (SP) must be 2% above the CP.
SP=100+2=102
Calculate Required Discount
The discount is the difference between MP and SP. To find the percentage, divide this by MP and multiply by 100.
Discount%=120120−102×100=12018×100=15%
A is correct because a discount of 15% on a marked price of 120 results in a selling price of 102, which yields a profit of 2% on a cost price of 100.
This concept of markup and discount is fundamental to both Profit & Loss and Ratio-based Quantitative Aptitude problems, often appearing in compound scenarios involving successive discounts.
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