The price of sugar is reduced by 20%. Now a person can buy 500g more sugar for Rs. 36. The origInal price of the sugar per kilogram was

Options

A. Rs. 14.40
B. Rs. 18
C. Rs. 15.60
D. Rs. 16.50

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Calculate the New Price
Since the price of sugar is reduced by 20%, the new price of sugar per kilogram becomes:
\[ \text{New Price} = x - 0.2x = 0.8x = \frac{4}{5}x \]

### Step 3: Set Up the Equation
According to the problem, with the new price, a person can buy 500 grams more sugar for Rs. 36. We need to express this in terms of kilograms:
\[ 500 \text{ grams} = 0.5 \text{ kg} \]
Let’s denote the quantity of sugar that could be bought at the original price for Rs. 36 as \( Q_1 \) and the quantity that can be bought at the new price as \( Q_2 \).

The quantity of sugar that can be bought at the original price \( Q_1 \) is:
\[ Q_1 = \frac{36}{x} \]
The quantity of sugar that can be bought at the new price \( Q_2 \) is:
\[ Q_2 = \frac{36}{\frac{4}{5}x} = \frac{36 \times 5}{4x} = \frac{180}{4x} = \frac{45}{x} \]

### Step 4: Set Up the Equation for the Extra Sugar
According to the problem, the difference in the quantity of sugar bought at the new price and the original price is 0.5 kg:
\[ Q_2 - Q_1 = 0.5 \]
Substituting the expressions for \( Q_1 \) and \( Q_2 \):
\[ \frac{45}{x} - \frac{36}{x} = 0.5 \]

### Step 5: Simplify the Equation
Combining the fractions:
\[ \frac{45 - 36}{x} = 0.5 \]
\[ \frac{9}{x} = 0.5 \]

### Step 6: Solve for \( x \)
Cross-multiplying gives:
\[ 9 = 0.5x \]
\[ x = \frac{9}{0.5} = 18 \]

### Conclusion
The original price of sugar per kilogram was \( 18 \) rupees.

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