A man sells 30 apples for the cost price of 40 apples. His profit percentage (correct to two places of decimal) is:

Options

A. `33.33%`
B. `25.00%`
C. `30.67%`
D. `40.33%`

Answer

To solve the problem of finding the profit percentage when a man sells 30 apples for the cost price of 40 apples, we can follow these steps:

### Step 1: Define the Cost Price (CP) of One Apple
Let the cost price of one apple be \( CP \).

### Step 2: Calculate the Total Cost Price for 30 Apples
The cost price of 30 apples will be:
\[ \text{Total CP for 30 apples} = 30 \times CP \]

### Step 3: Calculate the Selling Price (SP) of 30 Apples
According to the problem, the man sells 30 apples for the cost price of 40 apples. Thus, the selling price of 30 apples is:
\[ \text{Total SP for 30 apples} = 40 \times CP \]

### Step 4: Calculate the Profit
Profit is calculated as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]
Substituting the values we calculated:
\[ \text{Profit} = (40 \times CP) - (30 \times CP) = 10 \times CP \]

### Step 5: Calculate the Profit Percentage
Profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{10 \times CP}{30 \times CP} \right) \times 100 \]
The \( CP \) cancels out:
\[ \text{Profit Percentage} = \left( \frac{10}{30} \right) \times 100 = \frac{1}{3} \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = 33.33\% \]

### Final Answer
The profit percentage is \( 33.33\% \).

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