The selling price of 15 items equals the cost of 20 items. What is the percentage profit enarned by the seller?

Options

A. 15
B. 20
C. 25
D. 33.3

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Variables
Let the cost price (CP) of one item be \( x \). Therefore, the cost price of 20 items will be \( 20x \).

### Step 2: Establish the Selling Price
Let the selling price (SP) of one item be \( z \). Therefore, the selling price of 15 items will be \( 15z \).

### Step 3: Set Up the Equation
According to the problem, the selling price of 15 items equals the cost price of 20 items. Therefore, we can write the equation:
\[ 15z = 20x \]

### Step 4: Solve for Selling Price
From the equation \( 15z = 20x \), we can express \( z \) in terms of \( x \):
\[ z = \frac{20x}{15} = \frac{4x}{3} \]

### Step 5: Calculate the Profit
The profit earned on one item can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = z - x \]
Substituting the value of \( z \):
\[ \text{Profit} = \frac{4x}{3} - x = \frac{4x}{3} - \frac{3x}{3} = \frac{x}{3} \]

### Step 6: Calculate the Percentage Profit
The percentage profit is given by the formula:
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Profit} = \left( \frac{\frac{x}{3}}{x} \right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
The percentage profit earned by the seller is \( 33.33\% \).

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