If the cost price of 12 articles be equal to the selling price of 10 articles, then find the profit per cent in the transaction.

Options

A. 15
B. 20
C. 25
D. None of these

Answer

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

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
We are given that the cost price of 12 articles is equal to the selling price of 10 articles.

### Step 2: Let’s denote the Cost Price and Selling Price
Let the Cost Price of one article be \( CP \) and the Selling Price of one article be \( SP \).

### Step 3: Set up the equation based on the given information
According to the problem:
\[ 12 \times CP = 10 \times SP \]

### Step 4: Express SP in terms of CP
From the equation above, we can express \( SP \) in terms of \( CP \):
\[ SP = \frac{12 \times CP}{10} = 1.2 \times CP \]

### Step 5: Calculate the profit
Profit is calculated as:
\[ Profit = SP - CP \]
Substituting the expression for \( SP \):
\[ Profit = (1.2 \times CP) - CP = 0.2 \times CP \]

### Step 6: Calculate the profit percentage
Profit percentage is given by the formula:
\[ Profit \% = \left( \frac{Profit}{CP} \right) \times 100 \]
Substituting the profit we calculated:
\[ Profit \% = \left( \frac{0.2 \times CP}{CP} \right) \times 100 = 0.2 \times 100 = 20\% \]

### Conclusion
The profit percentage in the transaction is **20%**.

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