A shopkeeper purchased 510 eggs. at the rate of 20 per dozen. 30 eggs were broken on the way. In order to make a gain of 20%. He must sell the remainîng eggs at rate of.

Options

A. 22.5
B. 25.5
C. 26.5
D. 26

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Calculate the Total Cost of the Eggs
The shopkeeper purchased 510 eggs at the rate of 20 rupees per dozen.

1. **Calculate the number of dozens in 510 eggs:**
\[ \text{Number of dozens} = \frac{510}{12} = 42.5 \text{ dozens} \]

2. **Calculate the total cost:**
\[ \text{Total cost} = 42.5 \text{ dozens} \times 20 \text{ rupees/dozen} = 850 \text{ rupees} \]

### Step 2: Calculate the Number of Remaining Eggs
30 eggs were broken on the way.

1. **Calculate the remaining eggs:**
\[ \text{Remaining eggs} = 510 - 30 = 480 \text{ eggs} \]

### Step 3: Calculate the Selling Price for a 20% Gain
To achieve a 20% gain, we need to find the selling price for the remaining 480 eggs.

1. **Calculate the cost price per egg:**
\[ \text{Cost price per egg} = \frac{850 \text{ rupees}}{510 \text{ eggs}} \approx 1.6667 \text{ rupees/egg} \]

2. **Calculate the total cost price for the remaining eggs:**
\[ \text{Total cost price for remaining eggs} = 1.6667 \text{ rupees/egg} \times 480 \text{ eggs} = 800 \text{ rupees} \]

3. **Calculate the desired selling price for a 20% gain:**
\[ \text{Selling price} = \text{Total cost price} + 20\% \text{ of Total cost price} \]
\[ \text{Selling price} = 800 + 0.2 \times 800 = 800 + 160 = 960 \text{ rupees} \]

### Step 4: Calculate the Selling Price per Egg
1. **Calculate the selling price per egg:**
\[ \text{Selling price per egg} = \frac{960 \text{ rupees}}{480 \text{ eggs}} = 2 \text{ rupees/egg} \]

### Final Answer
The shopkeeper must sell the remaining eggs at the rate of **2 rupees per egg** to achieve a 20% gain.

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