If 0.8 x cost price = 0.6 x selling price, the what is the profit percentage?

Options

A. 33.33
B. 25
C. 20
D. 10

Answer

To solve the problem step by step, we will follow the given relationship between cost price (CP) and selling price (SP) and calculate the profit percentage.

### Step 1: Set up the equation
Given the equation:
\[ 0.8 \times \text{CP} = 0.6 \times \text{SP} \]

### Step 2: Solve for SP in terms of CP
To isolate SP, we can rearrange the equation:
\[ \text{SP} = \frac{0.8 \times \text{CP}}{0.6} \]

### Step 3: Simplify the expression
Now, simplify the fraction:
\[ \text{SP} = \frac{0.8}{0.6} \times \text{CP} \]
\[ \text{SP} = \frac{8}{6} \times \text{CP} \]
\[ \text{SP} = \frac{4}{3} \times \text{CP} \]

### Step 4: Calculate the profit
Profit is defined as:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the value of SP:
\[ \text{Profit} = \left(\frac{4}{3} \times \text{CP}\right) - \text{CP} \]
To combine the terms, express CP as a fraction:
\[ \text{Profit} = \frac{4}{3} \text{CP} - \frac{3}{3} \text{CP} \]
\[ \text{Profit} = \frac{4 - 3}{3} \text{CP} \]
\[ \text{Profit} = \frac{1}{3} \text{CP} \]

### Step 5: Calculate the profit percentage
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100\% \]
Substituting the expression for Profit:
\[ \text{Profit Percentage} = \left(\frac{\frac{1}{3} \text{CP}}{\text{CP}}\right) \times 100\% \]
The CP cancels out:
\[ \text{Profit Percentage} = \frac{1}{3} \times 100\% \]
\[ \text{Profit Percentage} = 33.33\% \]

### Final Answer
The profit percentage is **33.33%**.