An egg seller sells his eggs only in the packs of 3 eggs, 6 eggs, 9 eggs, 12 eggs etc., but the rate is not necessarily uniform. One day Raju (which is not the same egg seller) purchased at the rate of 3 eggs for a rupee and the next hour he purchased equal number of eggs at the rate of 6 eggs for a rupee. Next day he sold all the eggs at the rate of 9 eggs for ₹ 2. What is his percentage profit or loss?

Options

A. `10%` loss
B. `11.11%` loss
C. `3%` loss
D. `2.5%` profit

Answer

To solve the problem step by step, we will calculate the total cost of the eggs purchased by Raju and the total revenue from selling those eggs. Finally, we will determine the percentage profit or loss.

### Step 1: Calculate the total number of eggs purchased
Raju buys eggs in two transactions:
1. He buys 3 eggs for ₹1.
2. He buys an equal number of eggs at the rate of 6 eggs for ₹1.

Let’s denote the number of eggs he buys in the first transaction as \( x \).

From the first transaction:
- He buys 3 eggs for ₹1, so if he buys \( x \) eggs, the cost for \( x \) eggs is \( \frac{x}{3} \) rupees.

From the second transaction:
- He buys the same number of eggs \( x \) at the rate of 6 eggs for ₹1. Therefore, the cost for \( x \) eggs is \( \frac{x}{6} \) rupees.

Since he bought equal numbers of eggs in both transactions, we can assume \( x = 3 \) (the number of eggs in the first transaction).

Total eggs purchased:
- Total eggs = \( 3 + 3 = 6 \) eggs.

### Step 2: Calculate the total cost of the eggs
Now we calculate the total cost:
- Cost for the first transaction (3 eggs for ₹1): ₹1
- Cost for the second transaction (3 eggs for ₹0.50): ₹0.50

Total cost = ₹1 + ₹0.50 = ₹1.50.

### Step 3: Calculate the total revenue from selling the eggs
Next, Raju sells all the eggs the next day at the rate of 9 eggs for ₹2.

To find out how much he earns from selling 6 eggs:
- If 9 eggs are sold for ₹2, then the price per egg = \( \frac{2}{9} \) rupees.
- Therefore, for 6 eggs, the revenue = \( 6 \times \frac{2}{9} = \frac{12}{9} = \frac{4}{3} \) rupees.

### Step 4: Calculate profit or loss
Now we can determine if Raju made a profit or a loss:
- Total cost = ₹1.50
- Total revenue = ₹1.33 (or ₹4/3)

Since total revenue (₹1.33) is less than total cost (₹1.50), Raju incurs a loss.

Loss = Total Cost - Total Revenue = ₹1.50 - ₹1.33 = ₹0.17.

### Step 5: Calculate the percentage loss
To find the percentage loss:
\[ \text{Percentage Loss} = \left(\frac{\text{Loss}}{\text{Total Cost}}\right) \times 100 \]
\[ \text{Percentage Loss} = \left(\frac{0.17}{1.50}\right) \times 100 \approx 11.33\% \]

### Final Answer
Raju incurs a percentage loss of approximately **11.33%**.

---