Ritu purchased 2 `1/2` dozen eggs at the rate of Rs. 20 per dozen. She found that 6 eggs were rotten. She sold the remaining eggs at the rate of Rs. 22 per dozen. Then her profit or loss percent is :

Options

A. 12%loss
B. 12%profit
C. 10%loss
D. 10%profit

Answer

To solve the problem step by step, we will calculate the cost price (CP), selling price (SP), and then determine the profit or loss percentage.

### Step 1: Calculate the Cost Price (CP)
Ritu purchased \(2 \frac{1}{2}\) dozen eggs at the rate of Rs. 20 per dozen.

First, convert \(2 \frac{1}{2}\) dozen into an improper fraction:
\[ 2 \frac{1}{2} = \frac{5}{2} \text{ dozen} \]

Now, calculate the cost price:
\[ CP = \text{Number of dozens} \times \text{Cost per dozen} = \frac{5}{2} \times 20 = \frac{100}{2} = 50 \text{ Rs.} \]

### Step 2: Calculate the Number of Eggs
Since 1 dozen equals 12 eggs, the total number of eggs Ritu purchased is:
\[ \text{Total eggs} = 2 \frac{1}{2} \text{ dozen} \times 12 = \frac{5}{2} \times 12 = 30 \text{ eggs} \]

### Step 3: Calculate the Number of Good Eggs
Ritu found that 6 eggs were rotten. Therefore, the number of good eggs is:
\[ \text{Good eggs} = \text{Total eggs} - \text{Rotten eggs} = 30 - 6 = 24 \text{ eggs} \]

### Step 4: Calculate the Selling Price (SP)
Ritu sold the remaining 24 eggs at the rate of Rs. 22 per dozen. First, calculate how many dozens are in 24 eggs:
\[ \text{Dozens of good eggs} = \frac{24}{12} = 2 \text{ dozen} \]

Now, calculate the selling price:
\[ SP = \text{Number of dozens} \times \text{Selling price per dozen} = 2 \times 22 = 44 \text{ Rs.} \]

### Step 5: Calculate Profit or Loss
Now, we can find out whether Ritu made a profit or a loss:
\[ \text{Loss} = CP - SP = 50 - 44 = 6 \text{ Rs.} \]

### Step 6: Calculate Loss Percentage
To find the loss percentage, use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100 = \left(\frac{6}{50}\right) \times 100 = 12\% \]

### Final Answer
Ritu incurred a loss of 12%.

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