The ratio of the cost price and the selling price is `7:5.` The profit percent is -

Options

A. `10%`
B. `40%`
C. `25 %`
D. `30 %`

Answer

To find the profit percentage when the ratio of the cost price (CP) to the selling price (SP) is given as 7:5, we can follow these steps:

### Step 1: Understand the Ratio
The ratio of cost price to selling price is given as:
\[ CP : SP = 7 : 5 \]

### Step 2: Assign Variables
Let the cost price (CP) be \( 7x \) and the selling price (SP) be \( 5x \), where \( x \) is a common multiplier.

### Step 3: Calculate Profit
Profit is calculated as:
\[ \text{Profit} = SP - CP \]
Substituting the values we assigned:
\[ \text{Profit} = 5x - 7x = -2x \]
This indicates a loss, not a profit, since the result is negative.

### Step 4: Calculate Profit Percentage
The formula for profit percentage is:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{-2x}{7x} \right) \times 100 \]

### Step 5: Simplify the Expression
The \( x \) cancels out:
\[ \text{Profit Percentage} = \left( \frac{-2}{7} \right) \times 100 \]

### Step 6: Calculate the Final Value
Now, calculate:
\[ \text{Profit Percentage} = -\frac{200}{7} \approx -28.57\% \]

Since we are looking for profit percentage and we have a loss, we can conclude that there is a loss of approximately 28.57%.

### Final Answer
The profit percentage is **-28.57%** (indicating a loss).

---