A reduction of 15% in the price of sugar enables Aruna Rai to buy 6 kg more for Rs. 2272. The reduced price of sugar per kg is:

Options

A. Rs. 70.80
B. Rs. 6 0
C. Rs. 66.80
D. Rs. 62.50

Answer

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

### Step 1: Define Variables
Let the original price of sugar per kg be \( P \).

### Step 2: Calculate Reduced Price
Since there is a reduction of 15%, the reduced price of sugar per kg will be:
\[ \text{Reduced Price} = P - 0.15P = 0.85P \]

### Step 3: Set Up the Equation
According to the problem, with the reduced price, Aruna can buy 6 kg more for Rs. 2272. Therefore, the amount of sugar she could buy before the price reduction can be expressed as:
\[ \text{Quantity before reduction} = \frac{2272}{P} \]
And after the reduction:
\[ \text{Quantity after reduction} = \frac{2272}{0.85P} \]
Given that the quantity after reduction is 6 kg more than the quantity before reduction, we can write:
\[ \frac{2272}{0.85P} = \frac{2272}{P} + 6 \]

### Step 4: Solve the Equation
To eliminate the fractions, we can multiply through by \( 0.85P \):
\[ 2272 = 0.85 \times 2272 + 6 \times 0.85P \]
Calculating \( 0.85 \times 2272 \):
\[ 0.85 \times 2272 = 1931.2 \]
So, the equation becomes:
\[ 2272 = 1931.2 + 5.1P \]
Now, isolate \( P \):
\[ 2272 - 1931.2 = 5.1P \]
\[ 340.8 = 5.1P \]
Now, divide both sides by 5.1:
\[ P = \frac{340.8}{5.1} \approx 66.8 \]

### Step 5: Calculate the Reduced Price
Now, we can find the reduced price:
\[ \text{Reduced Price} = 0.85P = 0.85 \times 66.8 \approx 56.78 \]

### Final Answer
Thus, the reduced price of sugar per kg is approximately **Rs. 56.78**.

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