A fruit vendor purchased 90 dozens of bananas at Rs. 20 per dozen. Out of this, 18 dozens got rotten and he sold them at Rs 16 per dozen. Remaining bananas were sold by him at Rs. 24 per dozen. What profit did the make in this transaction?

Options

A. `12%`
B. `15%`
C. `20%`
D. `28%`

Answer

To solve the problem step by step, we will calculate the cost price, the selling price of the rotten bananas, the selling price of the remaining bananas, and finally determine the profit made by the fruit vendor.

### Step 1: Calculate the Cost Price (CP)
The vendor purchased 90 dozens of bananas at Rs. 20 per dozen.

\[ \text{Cost Price (CP)} = \text{Number of dozens} \times \text{Cost per dozen} \]
\[ \text{CP} = 90 \times 20 = Rs. 1800 \]

### Step 2: Calculate the Selling Price (SP) of the Rotten Bananas
Out of the 90 dozens, 18 dozens got rotten and were sold at Rs. 16 per dozen.

\[ \text{Selling Price of rotten bananas} = \text{Number of rotten dozens} \times \text{Selling price per dozen} \]
\[ \text{SP of rotten bananas} = 18 \times 16 = Rs. 288 \]

### Step 3: Calculate the Remaining Bananas
The remaining bananas after the rotten ones are:

\[ \text{Remaining dozens} = \text{Total dozens} - \text{Rotten dozens} \]
\[ \text{Remaining dozens} = 90 - 18 = 72 \text{ dozens} \]

### Step 4: Calculate the Selling Price (SP) of the Remaining Bananas
The remaining 72 dozens were sold at Rs. 24 per dozen.

\[ \text{Selling Price of remaining bananas} = \text{Remaining dozens} \times \text{Selling price per dozen} \]
\[ \text{SP of remaining bananas} = 72 \times 24 = Rs. 1728 \]

### Step 5: Calculate the Total Selling Price (SP)
Now, we will calculate the total selling price by adding the selling price of the rotten bananas and the remaining bananas.

\[ \text{Total SP} = \text{SP of rotten bananas} + \text{SP of remaining bananas} \]
\[ \text{Total SP} = 288 + 1728 = Rs. 2016 \]

### Step 6: Calculate the Profit
Profit can be calculated by subtracting the cost price from the total selling price.

\[ \text{Profit} = \text{Total SP} - \text{CP} \]
\[ \text{Profit} = 2016 - 1800 = Rs. 216 \]

### Step 7: Calculate the Profit Percentage
To find the profit percentage, we use the formula:

\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{216}{1800} \right) \times 100 = 12\% \]

### Final Answer
The profit made by the vendor in this transaction is **Rs. 216**, and the profit percentage is **12%**.

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