The cost price of goods, for a shopkeeper, was X. He marked them at 15% above the cost price. Finally, he sold the goods at a discount of 25% what is his profit/loss percentage?

Options

A. 15% Profit
B. 13% Loss
C. 13.75% Loss
D. 13.5% Profit

Answer

To solve the problem step by step, let's follow the calculations based on the information provided.

### Step 1: Determine the Cost Price (CP)
The cost price of the goods for the shopkeeper is given as \( X \). For simplicity, we can assume \( X = 100 \).

### Step 2: Calculate the Marked Price (MP)
The shopkeeper marks the goods at 15% above the cost price. Therefore, we calculate the marked price as follows:
\[ \text{Marked Price (MP)} = \text{Cost Price (CP)} + 15\% \text{ of CP} \]
\[ \text{MP} = 100 + 0.15 \times 100 = 100 + 15 = 115 \]

### Step 3: Calculate the Discount
The shopkeeper sells the goods at a discount of 25% on the marked price. We calculate the discount as follows:
\[ \text{Discount} = 25\% \text{ of MP} = 0.25 \times 115 \]
To find 25% of 115, we can divide 115 by 4:
\[ \text{Discount} = \frac{115}{4} = 28.75 \]

### Step 4: Calculate the Selling Price (SP)
Now, we can find the selling price by subtracting the discount from the marked price:
\[ \text{Selling Price (SP)} = \text{MP} - \text{Discount} = 115 - 28.75 = 86.25 \]

### Step 5: Determine Profit or Loss
Now, we compare the selling price with the cost price to determine if there is a profit or loss:
\[ \text{Cost Price (CP)} = 100 \]
\[ \text{Selling Price (SP)} = 86.25 \]
Since the selling price is less than the cost price, there is a loss.

### Step 6: Calculate the Loss Amount
We can calculate the loss amount as follows:
\[ \text{Loss} = \text{CP} - \text{SP} = 100 - 86.25 = 13.75 \]

### Step 7: Calculate the Loss Percentage
Finally, we can calculate the loss percentage using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{13.75}{100} \right) \times 100 = 13.75\% \]

### Final Answer
The shopkeeper incurs a loss of **13.75%**.

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