Due to an increase of 30% in the price of eggs,6 eggs less are available for Rs 7.80.The present rate of eggs per dozen is

Options

A. Rs 5.50
B. Rs 4.68
C. Rs 6.49
D. Rs 3.58

Answer

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

### Step 1: Understand the Problem
We know that due to a 30% increase in the price of eggs, we can buy 6 fewer eggs for Rs 7.80. We need to find the present rate of eggs per dozen.

### Step 2: Determine the Price Increase
The price increase is 30%. If the original price of eggs is \( P \), the new price will be:
\[ \text{New Price} = P + 0.30P = 1.30P \]

### Step 3: Establish the Relationship Between Price and Quantity
Let the original number of eggs that could be bought for Rs 7.80 be \( x \). After the price increase, we can buy \( x - 6 \) eggs for the same amount of money (Rs 7.80).

### Step 4: Set Up the Equation
Using the original price:
\[ \frac{7.80}{P} = x \quad \text{(original number of eggs)} \]
Using the new price:
\[ \frac{7.80}{1.30P} = x - 6 \quad \text{(new number of eggs)} \]

### Step 5: Solve for \( x \)
We can set the two equations equal to each other:
\[ \frac{7.80}{P} - 6 = \frac{7.80}{1.30P} \]
Multiply through by \( P \) and \( 1.30P \) to eliminate the denominators:
\[ 7.80 \cdot 1.30 - 6 \cdot 1.30P = 7.80 \]
This simplifies to:
\[ 10.14 - 7.80 = 6 \cdot 1.30P \]
\[ 2.34 = 7.80P \]

### Step 6: Solve for \( P \)
Now, divide both sides by 7.80:
\[ P = \frac{2.34}{7.80} = 0.30 \quad \text{(price per egg)} \]

### Step 7: Calculate the Price per Dozen
To find the price per dozen, multiply the price per egg by 12:
\[ \text{Price per dozen} = 0.30 \times 12 = 3.60 \]

### Final Answer
The present rate of eggs per dozen is Rs 3.60.

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