A person wants to reduce the trade tax, so he calculates his profit on the sale price instead of on the cost price. In this way by selling a article for ₹ 280 he calculates his profit as `14(2)/7` What is his actual profit percentage?

Options

A. `20%`
B. `16.66%`
C. `25%`
D. data insufficient

Answer

To solve the problem step by step, we need to find the actual profit percentage based on the information given.

### Step 1: Understand the given profit percentage
The person calculates his profit as \( \frac{14}{7} \) percent on the selling price. This simplifies to:
\[ \frac{14}{7} = 2\% \]
So, the profit percentage he is calculating is 2%.

### Step 2: Identify the selling price
The selling price (SP) of the article is given as ₹280.

### Step 3: Calculate the profit amount
Using the profit percentage calculated, we can find the profit amount. The profit amount (P) can be calculated as:
\[ P = \text{SP} \times \left(\frac{\text{Profit Percentage}}{100}\right) \]
Substituting the values:
\[ P = 280 \times \left(\frac{2}{100}\right) = 280 \times 0.02 = ₹5.6 \]

### Step 4: Calculate the cost price
Now, we can find the cost price (CP) using the formula:
\[ \text{CP} = \text{SP} - P \]
Substituting the values:
\[ \text{CP} = 280 - 5.6 = ₹274.4 \]

### Step 5: Calculate the actual profit
The actual profit is the difference between the selling price and the cost price:
\[ \text{Actual Profit} = \text{SP} - \text{CP} = 280 - 274.4 = ₹5.6 \]

### Step 6: Calculate the actual profit percentage
The actual profit percentage can be calculated using the formula:
\[ \text{Actual Profit Percentage} = \left(\frac{\text{Actual Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Actual Profit Percentage} = \left(\frac{5.6}{274.4}\right) \times 100 \approx 2.04\% \]

### Final Answer
The actual profit percentage is approximately **2.04%**.

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