If the cost price of 10 articles is equal to the selling price of 7 articles, then the gain or loss Percent is :

Options

A. 0.51
B. 42`6/7`%
C. 0.35
D. 42`6/7`%

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)
We know from the question that the cost price of 10 articles is equal to the selling price of 7 articles.

### Step 2: Set up the equations
Let the cost price of one article be \( CP \) and the selling price of one article be \( SP \). Therefore, we can write:
\[ 10 \times CP = 7 \times SP \]

### Step 3: Express CP in terms of SP
From the equation above, we can express \( CP \) in terms of \( SP \):
\[ CP = \frac{7}{10} \times SP \]

### Step 4: Calculate the Profit
Profit is defined as:
\[ Profit = SP - CP \]
Substituting the expression for \( CP \):
\[ Profit = SP - \frac{7}{10} \times SP = SP \left(1 - \frac{7}{10}\right) = SP \left(\frac{3}{10}\right) \]

### Step 5: Calculate the Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{Profit}{CP}\right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left(\frac{\frac{3}{10} \times SP}{\frac{7}{10} \times SP}\right) \times 100 \]
The \( SP \) cancels out:
\[ \text{Profit Percentage} = \left(\frac{3}{7}\right) \times 100 \]

### Step 6: Simplify the Profit Percentage
Now, we simplify:
\[ \text{Profit Percentage} = \frac{300}{7} \approx 42.86\% \]

### Conclusion
Thus, the gain percentage is approximately \( 42.86\% \).

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