Marked price of an article is 30% more than its cost price. If 30% discount is given, then what will be the loss percentage?

Options

A. A. 0
B. B. 9
C. C. 6
D. D. 8

Answer

To solve the problem step by step, we will first establish the relationship between the cost price (CP), marked price (MP), and selling price (SP).

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( x \).

### Step 2: Calculate the Marked Price
The marked price (MP) is 30% more than the cost price. Therefore, we can calculate the marked price as:
\[ MP = CP + 30\% \text{ of } CP = x + 0.3x = 1.3x \]

### Step 3: Calculate the Selling Price after Discount
A discount of 30% is given on the marked price. Thus, the selling price (SP) after applying the discount can be calculated as:
\[ SP = MP - 30\% \text{ of } MP = 1.3x - 0.3 \times 1.3x = 1.3x - 0.39x = 0.91x \]

### Step 4: Calculate the Loss
Now, we need to find the loss incurred in this transaction. The loss can be calculated as:
\[ \text{Loss} = CP - SP = x - 0.91x = 0.09x \]

### Step 5: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 = \left( \frac{0.09x}{x} \right) \times 100 = 9\% \]

### Conclusion
The loss percentage in this transaction is **9%**.