If the cost price of 20 articles is equal to the selling price of 18 articles, then find the profit per cent.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
The problem states that the cost price of 20 articles is equal to the selling price of 18 articles.

### Step 2: Define the Cost Price of One Article
Let's assume the cost price (CP) of one article is 1 rupee.

### Step 3: Calculate the Total Cost Price for 20 Articles
If the cost price of one article is 1 rupee, then the cost price of 20 articles will be:
\[ \text{CP of 20 articles} = 20 \times 1 = 20 \text{ rupees} \]

### Step 4: Set the Selling Price of 18 Articles
According to the problem, the selling price (SP) of 18 articles is equal to the cost price of 20 articles. Therefore:
\[ \text{SP of 18 articles} = 20 \text{ rupees} \]

### Step 5: Calculate the Selling Price of One Article
To find the selling price of one article, we can divide the total selling price of 18 articles by 18:
\[ \text{SP of 1 article} = \frac{20}{18} \text{ rupees} \]

### Step 6: Calculate the Profit
Profit (P) is calculated as:
\[ P = \text{SP} - \text{CP} \]
For one article:
\[ P = \frac{20}{18} - 1 \]
To simplify:
\[ P = \frac{20}{18} - \frac{18}{18} = \frac{2}{18} = \frac{1}{9} \text{ rupees} \]

### Step 7: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{P}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{\frac{1}{9}}{1} \right) \times 100 = \frac{100}{9} \approx 11.11\% \]

### Final Answer
The profit percentage is approximately **11.11%**.