A merchant fixes the sale price of his goods at 15% above the cost price. He sells his goods at 12% less than the fixed price.His percentage of profit is:

Options

A. 2 `1/2` %
B. 1 `1/5` %
C. 1 `1/2` %
D. 0.02

Answer

To solve the problem step by step, we will first define the variables and then calculate the percentage of profit based on the given information.

### Step 1: Define the Cost Price (CP)
Let the Cost Price (CP) of the goods be represented as \( CP \).

### Step 2: Calculate the Fixed Sale Price (SP)
The merchant fixes the sale price at 15% above the cost price. Therefore, the Fixed Sale Price (SP) can be calculated as:
\[ SP = CP + 0.15 \times CP = 1.15 \times CP \]

### Step 3: Calculate the Selling Price after Discount
The merchant sells the goods at 12% less than the fixed sale price. Thus, the Selling Price (SP') after the discount is:
\[ SP' = SP - 0.12 \times SP = SP \times (1 - 0.12) = SP \times 0.88 \]
Substituting the value of SP from Step 2:
\[ SP' = (1.15 \times CP) \times 0.88 = 1.012 \times CP \]

### Step 4: Calculate the Profit
The profit can be calculated as the difference between the Selling Price (SP') and the Cost Price (CP):
\[ \text{Profit} = SP' - CP = (1.012 \times CP) - CP = 0.012 \times CP \]

### Step 5: Calculate the Percentage of Profit
The percentage of profit is given by the formula:
\[ \text{Percentage of Profit} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the profit from Step 4:
\[ \text{Percentage of Profit} = \left( \frac{0.012 \times CP}{CP} \right) \times 100 = 0.012 \times 100 = 1.2\% \]

### Final Answer
The percentage of profit is **1.2%**.

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