The government reduced the price of sugar by 15%. By this a consumer can buy 7.4 kg more sugar for Rs.1258. The original price per kg of sugar is?

Options

A. Rs. 25.5
B. Rs.30
C. Rs.27
D. Rs.28

Answer

To find the original price per kg of sugar, we can follow these steps:

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

### Step 2: Calculate the Reduced Price
The price is reduced by 15%. Therefore, the reduced price can be calculated as:
\[ \text{Reduced Price} = X \times \left(1 - \frac{15}{100}\right) = X \times \frac{85}{100} = \frac{17X}{20} \text{ rupees per kg} \]

### Step 3: Determine the Quantity of Sugar Bought
The amount of money spent is Rs. 1258. The quantity of sugar that can be bought at the reduced price is:
\[ \text{Quantity at Reduced Price} = \frac{1258}{\frac{17X}{20}} = \frac{1258 \times 20}{17X} = \frac{25160}{17X} \text{ kg} \]

### Step 4: Calculate the Original Quantity Bought
At the original price \( X \), the quantity of sugar bought would be:
\[ \text{Quantity at Original Price} = \frac{1258}{X} \text{ kg} \]

### Step 5: Set Up the Equation
According to the problem, the quantity bought at the reduced price is 7.4 kg more than the quantity bought at the original price:
\[ \frac{25160}{17X} = \frac{1258}{X} + 7.4 \]

### Step 6: Clear the Denominators
To eliminate the fractions, multiply the entire equation by \( 17X \):
\[ 25160 = 17 \times 1258 + 17 \times 7.4X \]

### Step 7: Calculate the Values
Now, calculate \( 17 \times 1258 \):
\[ 17 \times 1258 = 21386 \]
And calculate \( 17 \times 7.4 \):
\[ 17 \times 7.4 = 125.8 \]
So the equation becomes:
\[ 25160 = 21386 + 125.8X \]

### Step 8: Rearrange the Equation
Rearranging gives:
\[ 125.8X = 25160 - 21386 \]
Calculating the right side:
\[ 125.8X = 3774 \]

### Step 9: Solve for \( X \)
Now, divide both sides by 125.8:
\[ X = \frac{3774}{125.8} \approx 30 \]

### Conclusion
The original price per kg of sugar is approximately **Rs. 30**.

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