The selling price of 10 oranges is the cost price of 13 oranges. Then the profit percentage is

Options

A. `30%`
B. `10%`
C. `13%`
D. `3%`

Answer

To find the profit percentage based on the information given in the question, we can follow these steps:

### Step 1: Define Variables
Let the cost price (CP) of 1 orange be \( x \).

### Step 2: Calculate Selling Price (SP)
According to the question, the selling price of 10 oranges is equal to the cost price of 13 oranges. Therefore, we can express this as:
\[ \text{SP of 10 oranges} = \text{CP of 13 oranges} \]
This can be written mathematically as:
\[ 10 \times \text{SP of 1 orange} = 13 \times x \]

### Step 3: Express Selling Price of 1 Orange
Let the selling price of 1 orange be \( y \). From the equation above, we can express \( y \) as:
\[ 10y = 13x \implies y = \frac{13x}{10} \]

### Step 4: Calculate Profit
The profit made on selling 1 orange can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = y - x = \frac{13x}{10} - x \]
To simplify this, we find a common denominator:
\[ \text{Profit} = \frac{13x}{10} - \frac{10x}{10} = \frac{3x}{10} \]

### Step 5: Calculate Profit Percentage
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{\frac{3x}{10}}{x} \right) \times 100 = \left( \frac{3}{10} \right) \times 100 = 30\% \]

### Final Answer
Thus, the profit percentage is **30%**.

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