A dealer by selling 12 oranges gets the cost price of 15 oragnes. What is the percentage profit ?

Answer

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

### Step 1: Understand the relationship between selling price and cost price
The dealer sells 12 oranges for the cost price of 15 oranges. This means that the selling price (SP) of 12 oranges is equal to the cost price (CP) of 15 oranges.

### Step 2: Define the cost price and selling price
Let the cost price of one orange be \( CP \).
Then, the cost price of 15 oranges is:
\[ CP_{15} = 15 \times CP \]
The selling price of 12 oranges is:
\[ SP_{12} = SP \]

### Step 3: Set up the equation
According to the problem, we have:
\[ SP_{12} = CP_{15} \]
This can be written as:
\[ SP = 15 \times CP \]

### Step 4: Find the selling price of one orange
To find the selling price of one orange, we can express the selling price of 12 oranges in terms of the cost price:
\[ SP_{12} = 12 \times SP_{1} \]
Where \( SP_{1} \) is the selling price of one orange. Thus:
\[ 12 \times SP_{1} = 15 \times CP \]
From this, we can find \( SP_{1} \):
\[ SP_{1} = \frac{15 \times CP}{12} \]

### Step 5: Calculate the profit
The profit made on selling one orange can be calculated as:
\[ \text{Profit} = SP_{1} - CP = \frac{15 \times CP}{12} - CP \]
To simplify this, we can express \( CP \) with a common denominator:
\[ \text{Profit} = \frac{15 \times CP}{12} - \frac{12 \times CP}{12} = \frac{3 \times CP}{12} = \frac{CP}{4} \]

### Step 6: Calculate the percentage profit
The percentage profit is given by the formula:
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the profit we found:
\[ \text{Percentage Profit} = \left( \frac{\frac{CP}{4}}{CP} \right) \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Final Answer
The percentage profit is **25%**.

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