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A shopkeeper marks an item 50% above the cost price. If he allows a discount of 20% and makes a profit of 20%, what is the actual discount percentage applied?
20%
25%
15%
10%
20%
Assume Cost Price = 100. Then Marked Price = 150. Since Profit is 20%, Selling Price = 120. Calculate discount as (Marked Price - Selling Price) / Marked Price.
Marked price is 50% above cost price, discount percentage is 20%, and profit percentage is 20%.
Selling┬аPrice=Cost┬аPrice├Ч(1+Profit%)=Marked┬аPrice├Ч(1тИТDiscount%)
Assume Cost Price = 100. Then Marked Price = 150. Since Profit is 20%, Selling Price = 120. Calculate discount as (Marked Price - Selling Price) / Marked Price.
Students often incorrectly calculate the discount on the Cost Price instead of the Marked Price, leading to errors in the percentage base.
Define base values
Assume the Cost Price (CP) is 100. Since the item is marked 50% above CP, the Marked Price (MP) becomes 100+50=150.
CP=100,MP=100├Ч1.5=150
Calculate Selling Price
Given the profit percentage is 20%, the Selling Price (SP) is calculated based on the CP.
SP=100├Ч(1+0.20)=120
Determine the actual discount percentage
The discount amount is the difference between MP and SP. The discount percentage is calculated on the MP.
Discount=MPтИТSP=150тИТ120=30
Calculate percentage
Divide the discount amount by the MP to get the rate.
Discount%=15030тАЛ├Ч100=20%
A is correct because the calculated discount percentage on the marked price of 150 to reach a selling price of 120 is 20%.
This concept of relative percentages is essential for Data Interpretation questions in competitive exams where multiple percentage changes are applied sequentially.