A shopkeeper sells his goods at 22.5% profit on selling price. Find actual profit %?

Options

A. `29.03%`
B. `32.5%`
C. `26.37%`
D. `28.53%`

Answer

To find the actual profit percentage when a shopkeeper sells his goods at a 22.5% profit on the selling price, we can follow these steps:

### Step-by-Step Solution

1. **Assume Selling Price (SP)**:
Let's assume the selling price (SP) of the goods is Rs. 100.

**Hint**: Start by assuming a convenient value for the selling price to simplify calculations.

2. **Calculate Profit**:
The profit is given as 22.5% of the selling price.
\[ \text{Profit} = 22.5\% \text{ of } 100 = \frac{22.5}{100} \times 100 = Rs. 22.5 \]

**Hint**: Remember that profit percentage is always calculated on the selling price.

3. **Calculate Cost Price (CP)**:
The cost price can be calculated using the formula:
\[ \text{Cost Price} = \text{Selling Price} - \text{Profit} \]
Substituting the values:
\[ \text{Cost Price} = 100 - 22.5 = Rs. 77.5 \]

**Hint**: The cost price is what the shopkeeper originally paid for the goods, which can be found by subtracting the profit from the selling price.

4. **Calculate Actual Profit Percentage**:
The actual profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{22.5}{77.5} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = 29.03\% \]

**Hint**: To find the profit percentage, always divide the profit by the cost price and multiply by 100.

### Final Answer
The actual profit percentage is **29.03%**.