Due to an increment of `50%` in the price of egg a person is able to buy 4 eggs less for Rs. 24. Find the initial cost of per dozen egg?

Answer

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

### Step 1: Define the variables
Let the initial price of one egg be \( x \) rupees.

### Step 2: Calculate the new price after the increment
Since the price of eggs has increased by 50%, the new price of one egg will be:
\[ \text{New Price} = x + 0.5x = 1.5x \]

### Step 3: Determine the number of eggs bought before and after the price increase
Before the price increase, the number of eggs that can be bought for Rs. 24 is:
\[ \text{Number of eggs before} = \frac{24}{x} \]

After the price increase, the number of eggs that can be bought for Rs. 24 is:
\[ \text{Number of eggs after} = \frac{24}{1.5x} \]

### Step 4: Set up the equation based on the information given
According to the problem, the person is able to buy 4 eggs less after the price increase. Therefore, we can set up the equation:
\[ \frac{24}{x} - \frac{24}{1.5x} = 4 \]

### Step 5: Solve the equation
First, simplify the left side:
\[ \frac{24}{x} - \frac{24}{1.5x} = \frac{24}{x} - \frac{24 \cdot 2}{3x} = \frac{24}{x} - \frac{16}{x} = \frac{8}{x} \]
So the equation becomes:
\[ \frac{8}{x} = 4 \]

Now, cross-multiply to solve for \( x \):
\[ 8 = 4x \implies x = \frac{8}{4} = 2 \]

### Step 6: Find the initial cost per dozen eggs
Since \( x \) is the cost of one egg, the cost of one dozen (12 eggs) will be:
\[ \text{Cost per dozen} = 12 \times x = 12 \times 2 = 24 \text{ rupees} \]

### Final Answer
The initial cost of per dozen eggs is Rs. 24.

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