A trader buys an article at `80%` of its marked price and sells it at `10%` discount on its marked price. His percentage profit is:

Options

A. `10^(1/2)`
B. 10
C. `12^(1/2)`
D. 15

Answer

To solve the problem step by step, let's define the variables and calculate the required values.

### Step 1: Define the Marked Price (MP)
Let's assume the marked price (MP) of the article is `100` (this is a convenient value to work with).

### Step 2: Calculate the Cost Price (CP)
The trader buys the article at `80%` of its marked price. Therefore, the cost price (CP) can be calculated as follows:
\[ CP = 80\% \text{ of MP} = 80\% \text{ of } 100 = \frac{80}{100} \times 100 = 80 \]

### Step 3: Calculate the Selling Price (SP)
The trader sells the article at a `10%` discount on its marked price. Therefore, the selling price (SP) can be calculated as follows:
\[ SP = MP - (10\% \text{ of MP}) = 100 - (10\% \text{ of } 100) = 100 - 10 = 90 \]

### Step 4: Calculate the Profit
The profit can be calculated using the formula:
\[ \text{Profit} = SP - CP = 90 - 80 = 10 \]

### Step 5: Calculate the Percentage Profit
The percentage profit can be calculated using the formula:
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{10}{80} \right) \times 100 = 12.5\% \]

### Final Answer
The percentage profit is **12.5%**.

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