After selling 4 article for Rs 1 a person incurred loss of 4 % if he had sold 3 article for Rs 1 his profit would be?

Options

A. 20%
B. 25%
C. 27%
D. 28%

Answer

To solve the problem step by step, we need to analyze the information given and calculate the required profit when selling 3 articles for Rs 1.

### Step 1: Determine the Cost Price (CP) of 4 articles
Given that selling 4 articles for Rs 1 incurs a loss of 4%, we can find the Cost Price (CP) of these articles.

Let the Cost Price of 4 articles be \( CP \).

Since there is a loss of 4%, the Selling Price (SP) is 96% of the Cost Price. Therefore, we can write:

\[ SP = CP - \text{Loss} = CP - 0.04 \times CP = 0.96 \times CP \]

Given that the Selling Price (SP) for 4 articles is Rs 1, we have:

\[ 0.96 \times CP = 1 \]

### Step 2: Calculate the Cost Price (CP)
To find the Cost Price (CP), we rearrange the equation:

\[ CP = \frac{1}{0.96} = \frac{100}{96} = \frac{25}{24} \text{ Rs for 4 articles} \]

### Step 3: Calculate the Cost Price (CP) for 1 article
Now, we need to find the Cost Price for 1 article:

\[ CP \text{ for 1 article} = \frac{CP \text{ for 4 articles}}{4} = \frac{25/24}{4} = \frac{25}{96} \text{ Rs} \]

### Step 4: Determine Selling Price (SP) when selling 3 articles for Rs 1
If he sells 3 articles for Rs 1, the Selling Price for 1 article is:

\[ SP \text{ for 1 article} = \frac{1}{3} \text{ Rs} \]

### Step 5: Calculate the Profit
Now, we can calculate the profit made when selling 3 articles for Rs 1.

Profit is calculated as:

\[ \text{Profit} = SP - CP \]

For 3 articles:

\[ \text{Profit for 3 articles} = \left(\frac{1}{3}\right) - \left(\frac{25}{96}\right) \]

To perform this calculation, we need a common denominator:

The least common multiple of 3 and 96 is 96. Thus:

\[ \frac{1}{3} = \frac{32}{96} \]

Now, substituting back into the profit formula:

\[ \text{Profit for 3 articles} = \frac{32}{96} - \frac{25}{96} = \frac{32 - 25}{96} = \frac{7}{96} \text{ Rs} \]

### Step 6: Calculate the Profit Percentage
To find the profit percentage, we use the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]

The Cost Price for 3 articles is:

\[ CP \text{ for 3 articles} = 3 \times \frac{25}{96} = \frac{75}{96} \]

Now substituting into the profit percentage formula:

\[ \text{Profit Percentage} = \left(\frac{\frac{7}{96}}{\frac{75}{96}}\right) \times 100 = \left(\frac{7}{75}\right) \times 100 \]

Calculating this gives:

\[ \text{Profit Percentage} = \frac{700}{75} \approx 9.33\% \]

### Final Result
The profit when selling 3 articles for Rs 1 is approximately \( \frac{7}{96} \) Rs, and the profit percentage is approximately \( 9.33\% \).

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