A shopkeeper calculate his profit per cent on the selling price which comes out to be 30%. If if had been calculated as usual on the cost price then what is the requrired percentage profit?

Options

A. `42 6/7%`
B. `4 7/27 %`
C. `7 6/42 %`
D. none of these

Answer

To solve the problem step by step, we will first understand the relationship between selling price (SP), cost price (CP), and profit percentage.

### Step-by-Step Solution:

1. **Assume Selling Price (SP)**:
Let's assume the selling price (SP) is 100. This is a common practice to simplify calculations.

**Hint**: Start by assuming a value for the selling price to make calculations easier.

2. **Calculate Profit**:
The profit percentage calculated on the selling price is 30%. This means that the profit is 30% of the selling price.
\[ \text{Profit} = \frac{30}{100} \times 100 = 30 \]

**Hint**: Use the formula for profit percentage to find the actual profit amount.

3. **Calculate Cost Price (CP)**:
Now, we can find the cost price (CP) using the formula:
\[ \text{CP} = \text{SP} - \text{Profit} \]
Substituting the values we have:
\[ \text{CP} = 100 - 30 = 70 \]

**Hint**: Remember that the cost price is the selling price minus the profit.

4. **Calculate Profit Percentage on Cost Price**:
Now we need to calculate the profit percentage based on the cost price. The formula for profit percentage is:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{30}{70}\right) \times 100 \]

**Hint**: Use the profit and cost price to find the profit percentage.

5. **Simplify the Calculation**:
Now, simplifying the above expression:
\[ \text{Profit Percentage} = \frac{3000}{70} \approx 42.86\% \]

**Hint**: Perform the division carefully to get the final profit percentage.

### Final Answer:
The required profit percentage when calculated on the cost price is approximately **42.86%**.