An unscrupulous trader steals 4 bananas for every dozen whenever he purchases them from a farmer and his customers steal 2 bananas for every dozen whenever they parchase the bananas from this trader. What is the profit or loss percentage of the trader, if he sells the bananas at the price that is offered by the farmer?

Options

A. 16.67 loss
B. 22.22 profit
C. 14.28 profit
D. 12.5 loss

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Understanding the Purchase
The trader buys bananas from the farmer. For every dozen (12 bananas), he pays a certain price. Let's assume the price for 1 dozen (12 bananas) is 12 rupees.

### Step 2: Calculating the Actual Bananas Received
When the trader buys 1 dozen bananas, he steals 4 additional bananas. Therefore, instead of receiving just 12 bananas, he actually receives:
\[ 12 + 4 = 16 \text{ bananas} \]

### Step 3: Cost per Banana
The cost for the trader to acquire these 16 bananas is 12 rupees. Therefore, the cost per banana is:
\[ \text{Cost per banana} = \frac{12 \text{ rupees}}{16 \text{ bananas}} = 0.75 \text{ rupees per banana} \]

### Step 4: Understanding the Sale to Customers
When the trader sells bananas, he sells them at the price offered by the farmer, which is 12 rupees for 1 dozen (12 bananas). However, when a customer buys a dozen bananas, they actually take 2 extra bananas. Therefore, the customer receives:
\[ 12 + 2 = 14 \text{ bananas} \]

### Step 5: Revenue from Selling Bananas
The trader sells 14 bananas for 12 rupees. Hence, the revenue from selling these 14 bananas is:
\[ \text{Revenue} = 12 \text{ rupees} \]

### Step 6: Calculating the Effective Selling Price per Banana
The effective selling price per banana when selling 14 bananas for 12 rupees is:
\[ \text{Selling price per banana} = \frac{12 \text{ rupees}}{14 \text{ bananas}} \approx 0.857 \text{ rupees per banana} \]

### Step 7: Calculating Profit
Now, we can calculate the profit made by the trader on each banana sold:
\[ \text{Profit per banana} = \text{Selling price per banana} - \text{Cost per banana} \]
\[ = 0.857 - 0.75 = 0.107 \text{ rupees per banana} \]

### Step 8: Calculating Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{0.107}{0.75} \right) \times 100 \approx 14.27\% \]

### Conclusion
The trader makes a profit of approximately **14.27%**.

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