If the cost price of an article is 35% of the selling price, what is the profit per cent?

Options

A. 185.71
B. 212.36
C. 144.42
D. 110.11

Answer

To find the profit percentage when the cost price (CP) of an article is 35% of the selling price (SP), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between CP and SP**:
We know that the cost price (CP) is 35% of the selling price (SP). This can be expressed mathematically as:
\[ CP = \frac{35}{100} \times SP \]

2. **Express CP in terms of SP**:
Simplifying the equation gives:
\[ CP = 0.35 \times SP \]

3. **Find the ratio of CP to SP**:
To find the ratio of CP to SP, we can express it as:
\[ \frac{CP}{SP} = \frac{0.35 \times SP}{SP} = 0.35 \]
This can also be expressed as:
\[ \frac{CP}{SP} = \frac{35}{100} = \frac{7}{20} \]

4. **Calculate the profit**:
The profit (P) is defined as:
\[ P = SP - CP \]
Substituting the expression for CP:
\[ P = SP - 0.35 \times SP = 0.65 \times SP \]

5. **Calculate profit percentage**:
Profit percentage (Profit %) is calculated using the formula:
\[ \text{Profit \%} = \left(\frac{P}{CP}\right) \times 100 \]
Substituting the values we have:
\[ \text{Profit \%} = \left(\frac{0.65 \times SP}{0.35 \times SP}\right) \times 100 \]
The SP cancels out:
\[ \text{Profit \%} = \left(\frac{0.65}{0.35}\right) \times 100 \]

6. **Simplify the fraction**:
Now, simplifying \(\frac{0.65}{0.35}\):
\[ \frac{0.65}{0.35} = \frac{65}{35} = \frac{13}{7} \]

7. **Calculate the final profit percentage**:
Now substituting back into the profit percentage formula:
\[ \text{Profit \%} = \left(\frac{13}{7}\right) \times 100 \approx 185.71\% \]

### Final Answer:
The profit percentage is approximately **185.71%**.