A shopkeeper purchased 510 egg at the rate of Rs 20 per dozen. 30 eggs were broken on the way. In order to make a gain of 20%, he must sell the remaining eggs at the rate of

Options

A. Rs 22.50 per dozen
B. Rs 25.50 per dozen
C. Rs 26 per dozen
D. Rs 26.50 per dozen

Answer

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

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

1 dozen = 12 eggs, so:
- Cost per egg = Rs 20 / 12 = Rs 1.67 (approximately).

To find the total cost price (CP) for 510 eggs:
- Total CP = Number of eggs × Cost per egg
- Total CP = 510 × (20 / 12) = 510 × (5/3) = Rs 850.

### Step 2: Calculate the Number of Eggs Remaining After Breakage
The shopkeeper had 510 eggs, but 30 eggs were broken on the way.

- Remaining eggs = Total eggs - Broken eggs
- Remaining eggs = 510 - 30 = 480 eggs.

### Step 3: Calculate the Selling Price Required for a 20% Gain
To find the selling price (SP) needed to achieve a 20% gain, we first calculate the desired profit.

- Desired profit = 20% of Total CP
- Desired profit = 20/100 × 850 = Rs 170.

Now, we can calculate the total selling price needed to achieve this profit:
- Total SP = Total CP + Desired profit
- Total SP = 850 + 170 = Rs 1020.

### Step 4: Calculate the Selling Price Per Egg
Now, we need to find the selling price per egg for the remaining 480 eggs.

- Selling price per egg = Total SP / Remaining eggs
- Selling price per egg = 1020 / 480 = Rs 2.125 (approximately).

### Final Answer
The shopkeeper must sell the remaining eggs at the rate of approximately Rs 2.13 per egg to achieve a 20% gain.

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