If the cost price of 10 articles is equal to the selling price of 8 articles, then gain percent is

Options

A. 0.1
B. 0.08
C. 0.5
D. 0.25

Answer

To solve the problem, we need to determine the gain percent based on the relationship between the cost price (CP) and selling price (SP) of the articles. Here’s a step-by-step solution:

### Step 1: Define the Cost Price and Selling Price
Let the cost price of one article be \( CP \).
Then, the cost price of 10 articles is:
\[ \text{Cost Price of 10 articles} = 10 \times CP = 10CP \]

Let the selling price of one article be \( SP \).
Then, the selling price of 8 articles is:
\[ \text{Selling Price of 8 articles} = 8 \times SP = 8SP \]

According to the problem, the cost price of 10 articles is equal to the selling price of 8 articles:
\[ 10CP = 8SP \]

### Step 2: Express Selling Price in Terms of Cost Price
From the equation \( 10CP = 8SP \), we can express \( SP \) in terms of \( CP \):
\[ SP = \frac{10CP}{8} = \frac{5CP}{4} \]

### Step 3: Calculate the Profit
Profit is calculated as the difference between the selling price and the cost price:
\[ \text{Profit} = SP - CP \]
Substituting the value of \( SP \):
\[ \text{Profit} = \frac{5CP}{4} - CP \]
To combine the terms, we can express \( CP \) as \( \frac{4CP}{4} \):
\[ \text{Profit} = \frac{5CP}{4} - \frac{4CP}{4} = \frac{1CP}{4} = \frac{CP}{4} \]

### Step 4: Calculate the Gain Percent
Gain percent is calculated using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the profit we calculated:
\[ \text{Gain Percent} = \left( \frac{\frac{CP}{4}}{CP} \right) \times 100 \]
This simplifies to:
\[ \text{Gain Percent} = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Final Answer
The gain percent is \( 25\% \).

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