Due to an increase of 20% in the price of eggs, 2 eggs less are available for 24. The present rate of eggs per dozen is

Options

A. 25
B. 26.2
C. 27.8
D. 28.8

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step-by-Step Solution:

1. **Understand the Price Increase**:
- Let the original price of eggs be \( P \).
- After a 20% increase, the new price becomes \( P + 0.2P = 1.2P \).

2. **Determine the Quantity of Eggs**:
- Initially, for \( 24 \) rupees, the number of eggs we could buy at the original price \( P \) is:
\[ \text{Number of eggs} = \frac{24}{P} \]
- After the price increase, the number of eggs we can buy for the same \( 24 \) rupees is:
\[ \text{Number of eggs} = \frac{24}{1.2P} \]

3. **Set Up the Equation**:
- According to the problem, after the price increase, we can buy \( 2 \) eggs less:
\[ \frac{24}{P} - \frac{24}{1.2P} = 2 \]

4. **Simplify the Equation**:
- To simplify, find a common denominator:
\[ \frac{24(1.2) - 24}{1.2P} = 2 \]
- This simplifies to:
\[ \frac{24(0.2)}{1.2P} = 2 \]
- Which further simplifies to:
\[ \frac{4.8}{1.2P} = 2 \]

5. **Cross-Multiply to Solve for \( P \)**:
- Cross-multiplying gives:
\[ 4.8 = 2 \times 1.2P \]
- Thus:
\[ 4.8 = 2.4P \]
- Solving for \( P \):
\[ P = \frac{4.8}{2.4} = 2 \]

6. **Calculate the Present Rate per Dozen**:
- The cost of 1 egg is \( 2 \) rupees.
- Therefore, the cost of a dozen eggs (12 eggs) is:
\[ \text{Cost per dozen} = 2 \times 12 = 24 \text{ rupees} \]

### Final Answer:
The present rate of eggs per dozen is **24 rupees**.