The cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

Options

A. 18
B. 30
C. 24
D. 25

Answer

To solve the problem, we need to find the value of \( x \) given that the cost price of 30 articles is equal to the selling price of \( x \) articles and the profit is 25%.

### Step-by-Step Solution:

1. **Let the Cost Price (CP) of 1 article be \( C \)**:
- Therefore, the cost price of 30 articles = \( 30C \).

2. **Calculate the Selling Price (SP) of 1 article**:
- Given that the profit is 25%, the selling price of 1 article can be calculated using the formula:
\[ SP = CP + \text{Profit} \]
- Profit is 25% of the cost price, so:
\[ \text{Profit} = 25\% \text{ of } C = \frac{25}{100} \times C = 0.25C \]
- Therefore, the selling price of 1 article is:
\[ SP = C + 0.25C = 1.25C \]

3. **Calculate the Selling Price of \( x \) articles**:
- The selling price of \( x \) articles is:
\[ SP \text{ of } x \text{ articles} = x \times SP \text{ of 1 article} = x \times 1.25C = 1.25xC \]

4. **Set the Cost Price of 30 articles equal to the Selling Price of \( x \) articles**:
- According to the problem, the cost price of 30 articles is equal to the selling price of \( x \) articles:
\[ 30C = 1.25xC \]

5. **Simplify the equation**:
- We can divide both sides of the equation by \( C \) (assuming \( C \neq 0 \)):
\[ 30 = 1.25x \]

6. **Solve for \( x \)**:
- To find \( x \), we can rearrange the equation:
\[ x = \frac{30}{1.25} \]
- To simplify \( \frac{30}{1.25} \):
\[ x = \frac{30 \times 100}{125} = \frac{3000}{125} = 24 \]

### Final Answer:
The value of \( x \) is \( 24 \).