When calculated over the selling price the profit percentage on selling an article is `25%` . What is the actual profit percentage ?

Options

A. `30%`
B. `35%`
C. `33(1)/(3)%`
D. `36 (2)/(3)%`

Answer

To solve the problem step by step, we will use the information given about the profit percentage calculated over the selling price.

### Step-by-Step Solution:

1. **Understanding the Profit Percentage**:
The profit percentage is given as 25% when calculated on the selling price (SP). This means:
\[ \text{Profit} = 25\% \text{ of SP} \]

2. **Expressing Profit in Terms of Selling Price**:
If we let the selling price (SP) be represented as \( SP \), then:
\[ \text{Profit} = 0.25 \times SP \]

3. **Relating Selling Price and Cost Price**:
The profit can also be expressed as:
\[ \text{Profit} = SP - CP \]
where \( CP \) is the cost price. Thus, we can set up the equation:
\[ SP - CP = 0.25 \times SP \]

4. **Rearranging the Equation**:
Rearranging the above equation gives:
\[ SP - 0.25 \times SP = CP \]
Simplifying this, we get:
\[ 0.75 \times SP = CP \]

5. **Expressing Selling Price in Terms of Cost Price**:
From the equation \( 0.75 \times SP = CP \), we can express SP in terms of CP:
\[ SP = \frac{CP}{0.75} = \frac{4}{3} \times CP \]

6. **Calculating Actual Profit Percentage**:
Now, we can find the actual profit percentage using the formula:
\[ \text{Profit Percentage} = \frac{\text{Profit}}{CP} \times 100 \]
Substituting for Profit:
\[ \text{Profit} = SP - CP = \left(\frac{4}{3} \times CP\right) - CP = \left(\frac{4}{3} - 1\right) \times CP = \left(\frac{4}{3} - \frac{3}{3}\right) \times CP = \frac{1}{3} \times CP \]

7. **Final Calculation**:
Now substituting back into the profit percentage formula:
\[ \text{Profit Percentage} = \frac{\frac{1}{3} \times CP}{CP} \times 100 = \frac{1}{3} \times 100 = \frac{100}{3} \approx 33.33\% \]

### Final Answer:
The actual profit percentage is \( 33 \frac{1}{3} \% \).

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