The cost price of 27 articles is same as the selling price of 18 articles. Whatis the profit percent?

Options

A. 0.4
B. 0.5
C. 0.3
D. 0.25

Answer

To solve the problem, we need to find the profit percentage based on the given information about the cost price (CP) and selling price (SP) of the articles.

### Step-by-step Solution:

1. **Understand the Relationship**:
We know that the cost price of 27 articles is equal to the selling price of 18 articles. This can be expressed mathematically as:
\[ CP_{27} = SP_{18} \]

2. **Express CP and SP**:
Let the cost price of one article be \( CP \) and the selling price of one article be \( SP \). Therefore, we can write:
\[ 27 \times CP = 18 \times SP \]

3. **Rearranging the Equation**:
To find the ratio of CP to SP, we rearrange the equation:
\[ \frac{CP}{SP} = \frac{18}{27} \]

4. **Simplifying the Ratio**:
Simplifying the fraction \( \frac{18}{27} \):
\[ \frac{CP}{SP} = \frac{2}{3} \]

5. **Finding SP in terms of CP**:
From the ratio \( \frac{CP}{SP} = \frac{2}{3} \), we can express SP in terms of CP:
\[ SP = \frac{3}{2} \times CP \]

6. **Calculating Profit**:
Profit is calculated as:
\[ Profit = SP - CP \]
Substituting the value of SP:
\[ Profit = \left(\frac{3}{2} \times CP\right) - CP = \frac{3}{2}CP - \frac{2}{2}CP = \frac{1}{2}CP \]

7. **Calculating Profit Percentage**:
The profit percentage is given by the formula:
\[ Profit\ Percentage = \left(\frac{Profit}{CP}\right) \times 100 \]
Substituting the profit we calculated:
\[ Profit\ Percentage = \left(\frac{\frac{1}{2}CP}{CP}\right) \times 100 = \frac{1}{2} \times 100 = 50\% \]

### Final Answer:
The profit percentage is **50%**.