A trader gains 12% after allowing a discount of 20% on the marked price of an article. Find his profit percentage if the article is sold at marked price allowing no discount.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 40%.
Let's assume the marked price of the article is "M."
When a discount of 20% is applied, the selling price becomes 80% (100% - 20%) of the marked price, which is 0.8M.
Given that the trader gains 12% after allowing this discount, we can set up the equation:
Selling Price - Cost Price = 12% of Cost Price
0.8M - Cost Price = 0.12 × Cost Price
0.8M = 1.12 × Cost Price
Cost Price = 0.8M/1.12
Cost Price = 0.7143M
Now, let's calculate the profit percentage when the article is sold at the marked price without any discount.
Profit = Selling Price - Cost Price
Profit = M - Cost Price
Profit = M - 0.7143M
Profit = 0.2857M
Profit Percentage = (Profit/Cost Price) × 100
Profit Percentage = (0.2857M/0.7143M) × 100
Profit Percentage = 0.4 × 100
Profit Percentage = 40%
Therefore, if the article is sold at the marked price without any discount, the trader's profit percentage is 40%.