52 oranges are bought for Rs 119.60 and sold at the rate of Rs 41.40 per dozen. The profit percentage is:

Options

A. `60%`
B. `45%`
C. `50%`
D. `40%`

Answer

To find the profit percentage from the given information, we will follow these steps:

### Step 1: Calculate the Cost Price (CP) of one orange
The total cost of 52 oranges is Rs 119.60. To find the cost price of one orange, we divide the total cost by the number of oranges.

\[ \text{Cost Price of one orange} = \frac{\text{Total Cost}}{\text{Number of Oranges}} = \frac{119.60}{52} \]

Calculating this gives:

\[ \text{Cost Price of one orange} = 2.30 \text{ Rs} \]

### Step 2: Calculate the Selling Price (SP) of one orange
The selling price is given as Rs 41.40 per dozen. Since one dozen equals 12 oranges, we need to find the selling price of one orange.

\[ \text{Selling Price of one orange} = \frac{\text{Selling Price per dozen}}{12} = \frac{41.40}{12} \]

Calculating this gives:

\[ \text{Selling Price of one orange} = 3.45 \text{ Rs} \]

### Step 3: Calculate the Profit
Profit can be calculated by subtracting the cost price from the selling price.

\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 3.45 - 2.30 \]

Calculating this gives:

\[ \text{Profit} = 1.15 \text{ Rs} \]

### Step 4: Calculate the Profit Percentage
Profit percentage is calculated using the formula:

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

Substituting the values we have:

\[ \text{Profit Percentage} = \left( \frac{1.15}{2.30} \right) \times 100 \]

Calculating this gives:

\[ \text{Profit Percentage} = 50\% \]

### Final Answer
The profit percentage is **50%**.

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