If the cost price of 20 articles is equal to the selling price of 15 articles, find the profit per cent.

Options

A. `33(1)/(2) %`
B. `33(1)/(3)%`
C. `33(1)/(5)%`
D. `33(1)/(7)%`

Answer

To solve the problem, we need to find the profit percentage when the cost price of 20 articles is equal to the selling price of 15 articles. Let's break this down step by step.

### Step 1: Define Variables
Let the cost price (CP) of one article be \( x \).
Then, the cost price of 20 articles is \( 20x \).

Let the selling price (SP) of one article be \( y \).
Then, the selling price of 15 articles is \( 15y \).

### Step 2: Set Up the Equation
According to the problem, the cost price of 20 articles is equal to the selling price of 15 articles:
\[ 20x = 15y \]

### Step 3: Express Selling Price in Terms of Cost Price
From the equation \( 20x = 15y \), we can express the selling price \( y \) in terms of the cost price \( x \):
\[ y = \frac{20x}{15} = \frac{4x}{3} \]

### Step 4: Calculate Profit
Profit is calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
For one article, the profit can be expressed as:
\[ \text{Profit} = y - x = \frac{4x}{3} - x \]
To simplify this, convert \( x \) to a fraction with a common denominator:
\[ \text{Profit} = \frac{4x}{3} - \frac{3x}{3} = \frac{4x - 3x}{3} = \frac{x}{3} \]

### Step 5: Calculate Profit Percentage
Profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the profit and cost price:
\[ \text{Profit Percentage} = \left( \frac{\frac{x}{3}}{x} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 = \frac{100}{3} \]

### Step 6: Convert to Decimal
Now, converting \( \frac{100}{3} \) to a decimal gives:
\[ \frac{100}{3} \approx 33.33\% \]

### Step 7: Final Answer
Thus, the profit percentage is:
\[ 33 \frac{1}{3}\% \text{ or } 33.33\% \]