If cost price is 35% of the selling price, what is the profit margin in percentage?

Options

A. `187.51%`
B. `183.35%`
C. `185.71%`
D. `181.75%`

Answer

To find the profit margin percentage when the cost price (CP) is 35% of the selling price (SP), we can follow these steps:

### Step 1: Define the relationship between CP and SP
Given that the cost price (CP) is 35% of the selling price (SP), we can express this mathematically:
\[ CP = 0.35 \times SP \]

### Step 2: Express SP in terms of CP
To find the selling price in terms of the cost price, we can rearrange the equation:
\[ SP = \frac{CP}{0.35} \]
This simplifies to:
\[ SP = \frac{CP \times 100}{35} = \frac{100}{35} \times CP \]

### Step 3: Calculate the ratio of SP to CP
Now, we can simplify \(\frac{100}{35}\):
\[ \frac{100}{35} = \frac{20}{7} \]
Thus, we can express the selling price as:
\[ SP = \frac{20}{7} \times CP \]

### Step 4: Calculate the profit
Profit (P) is defined as the difference between the selling price and the cost price:
\[ P = SP - CP \]
Substituting the expression for SP:
\[ P = \frac{20}{7} \times CP - CP \]
To combine the terms, we can express CP as \(\frac{7}{7} \times CP\):
\[ P = \left(\frac{20}{7} - \frac{7}{7}\right) \times CP = \frac{13}{7} \times CP \]

### Step 5: Calculate the profit percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{P}{CP}\right) \times 100 \]
Substituting the expression for profit:
\[ \text{Profit Percentage} = \left(\frac{\frac{13}{7} \times CP}{CP}\right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = \frac{13}{7} \times 100 \]

### Step 6: Perform the calculation
Now, we can calculate:
\[ \text{Profit Percentage} = \frac{1300}{7} \approx 185.71\% \]

### Conclusion
Thus, the profit margin percentage is approximately **185.71%**.

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