If profit is 1/`9^(th)` of selling price, then what is the profit percentage?

Options

A. A)11.11
B. B)12.5
C. C)14.28
D. D)14

Answer

To solve the problem step by step, we will derive the profit percentage given that the profit is \( \frac{1}{9} \) of the selling price (SP).

### Step 1: Understand the relationship between profit and selling price
Given that profit (P) is \( \frac{1}{9} \) of the selling price (SP), we can express this mathematically as:
\[ P = \frac{1}{9} \times SP \]

### Step 2: Express the selling price in terms of profit
From the equation above, we can rearrange it to find the selling price:
\[ SP = 9P \]

### Step 3: Calculate the cost price (CP)
The profit is defined as the difference between the selling price and the cost price:
\[ P = SP - CP \]
Substituting the expression for SP from Step 2:
\[ P = 9P - CP \]
Rearranging gives:
\[ CP = 9P - P = 8P \]

### Step 4: Calculate the profit percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{P}{CP} \right) \times 100 \]
Substituting the values of P and CP from the previous steps:
\[ \text{Profit Percentage} = \left( \frac{P}{8P} \right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = \left( \frac{1}{8} \right) \times 100 = 12.5\% \]

### Conclusion
Thus, the profit percentage is \( 12.5\% \).