By selling 4 articles for 1 rupee, a man loses 4%. Had he sold three articles per rupee, the profit would have been:

Options

A. A)30%
B. B) 28%
C. C) 16%
D. D) 12%

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Initial Situation
We know that a man sells 4 articles for 1 rupee and incurs a loss of 4%. This means that the cost price (CP) of the 4 articles is higher than the selling price (SP).

### Step 2: Calculate the Selling Price per Article
The selling price (SP) for 4 articles is 1 rupee. Therefore, the selling price per article is:
\[ \text{SP per article} = \frac{1 \text{ rupee}}{4} = 0.25 \text{ rupees} \]

### Step 3: Determine the Cost Price per Article
Since the man incurs a loss of 4%, we can use the formula for loss:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Given that the loss is 4%, we can express the selling price in terms of cost price:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Substituting the values:
\[ 0.25 = \text{CP} \times \left(1 - \frac{4}{100}\right) \]
\[ 0.25 = \text{CP} \times 0.96 \]
Now, solving for CP:
\[ \text{CP} = \frac{0.25}{0.96} \approx 0.2604 \text{ rupees} \]

### Step 4: Calculate the Selling Price if 3 Articles are Sold for 1 Rupee
If he sells 3 articles for 1 rupee, the selling price per article is:
\[ \text{SP per article} = \frac{1 \text{ rupee}}{3} \approx 0.3333 \text{ rupees} \]

### Step 5: Determine the Profit
Now we can calculate the profit using the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values:
\[ \text{Profit} = 0.3333 - 0.2604 \approx 0.0729 \text{ rupees} \]

### Step 6: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit \%} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit \%} = \left(\frac{0.0729}{0.2604}\right) \times 100 \approx 28\% \]

### Final Answer
Thus, if he had sold 3 articles for 1 rupee, the profit would have been **28%**.

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