On selling 23 articles a person gains profit equal to selling price of 3 articles. Find profit %.

Answer

To solve the problem step by step, we will follow the given information and apply the formulas for profit and profit percentage.

### Step 1: Understand the Given Information
We know that when a person sells 23 articles, the profit earned is equal to the selling price of 3 articles.

### Step 2: Define Variables
Let:
- SP = Selling Price of one article
- CP = Cost Price of one article

### Step 3: Calculate Total Selling Price (SP) and Profit
The total selling price for 23 articles is:
\[ \text{Total SP} = 23 \times SP \]

The profit earned from selling these 23 articles is equal to the selling price of 3 articles:
\[ \text{Profit} = 3 \times SP \]

### Step 4: Relate Profit to Cost Price
We know that:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]
Where Total CP for 23 articles is:
\[ \text{Total CP} = 23 \times CP \]

Substituting the values into the profit equation:
\[ 3 \times SP = (23 \times SP) - (23 \times CP) \]

### Step 5: Rearranging the Equation
Rearranging the equation gives:
\[ 23 \times CP = 23 \times SP - 3 \times SP \]
\[ 23 \times CP = 20 \times SP \]

### Step 6: Find Cost Price in Terms of Selling Price
Dividing both sides by 23:
\[ CP = \frac{20}{23} \times SP \]

### Step 7: Calculate Profit Percentage
Profit percentage is given by the formula:
\[ \text{Profit \%} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]

From our earlier steps, we know:
\[ \text{Profit} = 3 \times SP \]
Substituting CP:
\[ \text{Profit \%} = \left( \frac{3 \times SP}{\frac{20}{23} \times SP} \right) \times 100 \]

### Step 8: Simplifying the Profit Percentage
The SP cancels out:
\[ \text{Profit \%} = \left( \frac{3}{\frac{20}{23}} \right) \times 100 \]
\[ \text{Profit \%} = \left( \frac{3 \times 23}{20} \right) \times 100 \]
\[ \text{Profit \%} = \left( \frac{69}{20} \right) \times 100 \]
\[ \text{Profit \%} = 3.45 \times 100 \]
\[ \text{Profit \%} = 15\% \]

### Final Answer
The profit percentage is **15%**.

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