The Government reduced the price of sugar by 10 per cent. By this a consumer can buy 6.2 kg more sugar for 837. The re duced price per kg of sugar is

Options

A. 12.5
B. 13
C. 13.5
D. 14

Answer

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

### Step 1: Define the original price of sugar
Let the original price of sugar be \( P \) per kg. Since the government reduced the price by 10%, the new price becomes:
\[ \text{New Price} = P - 0.1P = 0.9P \]

### Step 2: Set up the equation for the amount of sugar bought
According to the problem, the consumer can buy 6.2 kg more sugar for 837 rupees after the price reduction. Therefore, we can express the amount of sugar bought before and after the price reduction as follows:

- Amount of sugar bought before the price reduction:
\[ \text{Amount before} = \frac{837}{P} \]

- Amount of sugar bought after the price reduction:
\[ \text{Amount after} = \frac{837}{0.9P} \]

### Step 3: Set up the equation based on the difference in quantity
The difference in the amount of sugar bought is given as 6.2 kg:
\[ \frac{837}{0.9P} - \frac{837}{P} = 6.2 \]

### Step 4: Simplify the equation
To simplify the left side, we can find a common denominator:
\[ \frac{837P - 837 \cdot 0.9P}{0.9P^2} = 6.2 \]
This simplifies to:
\[ \frac{837(1 - 0.9)}{0.9P^2} = 6.2 \]
\[ \frac{837 \cdot 0.1}{0.9P^2} = 6.2 \]

### Step 5: Solve for \( P^2 \)
Now, multiply both sides by \( 0.9P^2 \):
\[ 837 \cdot 0.1 = 6.2 \cdot 0.9P^2 \]
\[ 83.7 = 5.58P^2 \]
Now, divide both sides by 5.58:
\[ P^2 = \frac{83.7}{5.58} \approx 15 \]

### Step 6: Find the original price \( P \)
Taking the square root of both sides gives:
\[ P \approx \sqrt{15} \approx 3.87 \]

### Step 7: Calculate the reduced price
The reduced price is:
\[ \text{Reduced Price} = 0.9P \approx 0.9 \times 3.87 \approx 3.48 \]

### Final Answer
The reduced price per kg of sugar is approximately **3.48**.

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