The cost price of 50 articles is equal to the selling price of 40 articles. Gain percent is :

Options

A. `3 (9)/(17) %`
B. `15 (15)/(19) %`
C. `18 (3)/(4) %`
D. Rs. 1200

Answer

To solve the problem, we need to determine the gain percent based on the given information about the cost price (CP) and selling price (SP) of 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 \( CP \) and the selling price of one article be \( SP \).

From the problem, we know:
- The cost price of 50 articles = \( 50 \times CP \)
- The selling price of 40 articles = \( 40 \times SP \)

According to the problem statement:
\[ 50 \times CP = 40 \times SP \]

### Step 2: Express SP in terms of CP
We can rearrange the equation to express \( SP \) in terms of \( CP \):
\[ SP = \frac{50 \times CP}{40} \]
Simplifying this gives:
\[ SP = \frac{5}{4} \times CP \]

### Step 3: Calculate the Profit
The profit can be calculated using the formula:
\[ \text{Profit} = SP - CP \]
Substituting the expression for \( SP \):
\[ \text{Profit} = \left(\frac{5}{4} \times CP\right) - CP \]
To combine the terms, we can write \( CP \) as \( \frac{4}{4} \times CP \):
\[ \text{Profit} = \left(\frac{5}{4} \times CP - \frac{4}{4} \times CP\right) = \frac{1}{4} \times CP \]

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