A vender bought 40 dozen fruits for Rs 3,000. Out of these, 30 fruits were rotten and thrown away. At what rate (in Rs) per dozen should the vendor sell the remaining fruits to make a profit of `25%` in the entire transaction?

Options

A. 100
B. 80
C. 90
D. 75

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total number of fruits bought
The vendor bought 40 dozen fruits. Since 1 dozen equals 12 fruits, we can calculate the total number of fruits as follows:

\[ \text{Total fruits} = 40 \text{ dozen} \times 12 \text{ fruits/dozen} = 480 \text{ fruits} \]

**Hint:** Remember that 1 dozen is equal to 12 items.

### Step 2: Calculate the number of remaining fruits after discarding the rotten ones
The vendor found that 30 fruits were rotten and had to throw them away. Therefore, the number of remaining fruits is:

\[ \text{Remaining fruits} = 480 \text{ fruits} - 30 \text{ rotten fruits} = 450 \text{ fruits} \]

**Hint:** Subtract the number of rotten fruits from the total number of fruits to find the remaining fruits.

### Step 3: Convert the remaining fruits into dozens
To find out how many dozens of fruits are left, we divide the remaining fruits by 12:

\[ \text{Remaining dozens} = \frac{450 \text{ fruits}}{12 \text{ fruits/dozen}} = 37.5 \text{ dozen} \]

**Hint:** To convert fruits to dozens, divide the total number of fruits by 12.

### Step 4: Calculate the total cost of the fruits
The total cost of the fruits purchased was Rs 3,000.

**Hint:** The total cost is given in the problem statement.

### Step 5: Calculate the selling price for a 25% profit
To find the selling price (SP) for a 25% profit, we first need to calculate 25% of the total cost and then add it to the total cost:

\[ \text{Profit} = 25\% \text{ of } 3000 = \frac{25}{100} \times 3000 = 750 \]
\[ \text{Selling Price (SP)} = \text{Total Cost} + \text{Profit} = 3000 + 750 = 3750 \]

**Hint:** To calculate profit, find the percentage of the total cost and add it to the total cost for the selling price.

### Step 6: Calculate the selling price per dozen
Now, we need to find out at what rate per dozen the vendor should sell the remaining fruits to achieve this selling price:

\[ \text{Selling Price per dozen} = \frac{\text{Total Selling Price}}{\text{Remaining dozens}} = \frac{3750}{37.5} = 100 \]

**Hint:** Divide the total selling price by the number of dozens to find the price per dozen.

### Final Answer
The vendor should sell the remaining fruits at Rs 100 per dozen to make a profit of 25%.

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