By selling an article at 80% of its marked price, a trader makes a loss of 10%, what will be a profit percentage, if he sells it at 95% of its marked price?

Options

A. `6.9%`
B. 0.05
C. `5.9%`
D. `12.5%`

Answer

To solve the problem step by step, we need to find the profit percentage when the trader sells the article at 95% of its marked price, given that selling it at 80% of its marked price results in a 10% loss.

### Step 1: Define the Variables
Let:
- \( MP \) = Marked Price
- \( CP \) = Cost Price
- \( SP_1 \) = Selling Price at 80% of Marked Price
- \( SP_2 \) = Selling Price at 95% of Marked Price

### Step 2: Calculate Selling Price at 80% of Marked Price
From the problem, we know:
\[ SP_1 = 80\% \text{ of } MP = \frac{80}{100} \times MP = 0.8 \times MP \]

### Step 3: Relate Selling Price to Cost Price
Since selling at \( SP_1 \) results in a 10% loss, we can express this as:
\[ SP_1 = CP - 10\% \text{ of } CP = CP - 0.1 \times CP = 0.9 \times CP \]

### Step 4: Set Up the Equation
Now we can set the two expressions for \( SP_1 \) equal to each other:
\[ 0.8 \times MP = 0.9 \times CP \]

### Step 5: Rearranging the Equation
To find the relationship between \( MP \) and \( CP \), we rearrange the equation:
\[ \frac{MP}{CP} = \frac{0.9}{0.8} = \frac{9}{8} \]
This means:
\[ MP = \frac{9}{8} \times CP \]

### Step 6: Calculate Selling Price at 95% of Marked Price
Now, we calculate \( SP_2 \):
\[ SP_2 = 95\% \text{ of } MP = \frac{95}{100} \times MP = 0.95 \times MP \]

### Step 7: Substitute the Value of Marked Price
Using the relationship we found earlier:
\[ SP_2 = 0.95 \times \left(\frac{9}{8} \times CP\right) = \frac{95 \times 9}{8 \times 100} \times CP = \frac{855}{800} \times CP \]

### Step 8: Calculate Profit
To find the profit, we subtract the cost price from the selling price:
\[ \text{Profit} = SP_2 - CP = \left(\frac{855}{800} \times CP\right) - CP \]
\[ = \left(\frac{855}{800} - 1\right) \times CP = \left(\frac{855 - 800}{800}\right) \times CP = \frac{55}{800} \times CP \]

### Step 9: Calculate Profit Percentage
Now, we can find the profit percentage using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{\frac{55}{800} \times CP}{CP}\right) \times 100 = \frac{55}{800} \times 100 \]

### Step 10: Simplify the Profit Percentage
\[ = \frac{55 \times 100}{800} = \frac{5500}{800} = 6.875\% \]

### Final Answer
The profit percentage when selling at 95% of the marked price is approximately \( 6.9\% \).