Due to an increase of `30%` in the price of eggs, 3 eggs less are available for ₹ 9.10. The present rate per egg is :

Options

A. 91 paise
B. 78 paise
C. 48 paise
D. 84 paise

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We know that due to a 30% increase in the price of eggs, the number of eggs that can be bought for ₹9.10 has decreased by 3. We need to find the present rate per egg.

### Step 2: Let the Original Price per Egg be 'P'
Let the original price of one egg be \( P \). After a 30% increase, the new price per egg becomes:
\[ \text{New Price} = P + 0.3P = 1.3P \]

### Step 3: Determine the Number of Eggs Bought
Let the number of eggs that could be bought at the original price for ₹9.10 be \( N \). Therefore, we can express this as:
\[ N = \frac{9.10}{P} \]

After the price increase, the number of eggs that can be bought for ₹9.10 is \( N - 3 \):
\[ N - 3 = \frac{9.10}{1.3P} \]

### Step 4: Set Up the Equation
Substituting \( N \) in the equation gives us:
\[ \frac{9.10}{P} - 3 = \frac{9.10}{1.3P} \]

### Step 5: Clear the Denominators
To eliminate the fractions, multiply through by \( 1.3P \):
\[ 1.3 \cdot 9.10 - 3 \cdot 1.3P = 9.10 \]
This simplifies to:
\[ 11.83 - 3.9P = 9.10 \]

### Step 6: Solve for P
Rearranging the equation gives:
\[ 11.83 - 9.10 = 3.9P \]
\[ 2.73 = 3.9P \]
Now, divide both sides by 3.9:
\[ P = \frac{2.73}{3.9} \approx 0.7 \]

### Step 7: Find the Present Rate per Egg
Now, we need to find the present rate per egg, which is:
\[ \text{Present Rate} = 1.3P = 1.3 \times 0.7 \approx 0.91 \]

### Step 8: Final Answer
The present rate per egg is approximately ₹0.91.