What is percentage profit in selling an article at a discount of `20%` which was earlier being sold at a `40%` profit?

Options

A. `20%`
B. `14%`
C. `28%`
D. `12%`

Answer

To find the percentage profit when selling an article at a discount of 20% after initially selling it at a 40% profit, we can follow these steps:

### Step 1: Determine the Cost Price (CP)
Assume the cost price (CP) of the article is ₹100.

### Step 2: Calculate the Selling Price (SP) at 40% Profit
If the selling price at a 40% profit is calculated, we can find it as follows:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
\[ \text{Profit} = 40\% \text{ of CP} = \frac{40}{100} \times 100 = ₹40 \]
\[ \text{SP} = 100 + 40 = ₹140 \]

### Step 3: Calculate the Selling Price after 20% Discount
Now, we need to find the new selling price after applying a 20% discount on the selling price of ₹140:
\[ \text{Discount} = 20\% \text{ of SP} = \frac{20}{100} \times 140 = ₹28 \]
\[ \text{New Selling Price} = \text{SP} - \text{Discount} = 140 - 28 = ₹112 \]

### Step 4: Calculate the Profit from the New Selling Price
Now, we can calculate the profit when selling at the new selling price of ₹112:
\[ \text{Profit} = \text{New Selling Price} - \text{Cost Price} = 112 - 100 = ₹12 \]

### Step 5: Calculate the Percentage Profit
Finally, we calculate the percentage profit based on the new selling price:
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{12}{100} \right) \times 100 = 12\% \]

### Final Answer
The percentage profit when selling the article at a 20% discount after initially selling it at a 40% profit is **12%**.

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