The price of rice dropped by `25%` As a result Sita was able to buy 5 kg more rice for Rs.240. Find the original price of rice (in Rs./kg).

Options

A. 16
B. 18
C. 15
D. 20

Explanation

To solve the problem step by step, let's denote the original price of rice per kg as Rs. \( x \).

### Step 1: Determine the new price of rice after the drop
The price of rice dropped by 25%. Therefore, the new price of rice can be calculated as:
\[ \text{New Price} = x - \left( \frac{25}{100} \times x \right) = x - \frac{x}{4} = \frac{3x}{4} \]

### Step 2: Set up the equation based on the quantity of rice Sita can buy
According to the problem, Sita was able to buy 5 kg more rice for Rs. 240 after the price drop. Let’s denote the quantity of rice she could buy at the original price as \( Q \). Thus, at the original price, she could buy:
\[ Q = \frac{240}{x} \]
At the new price, she can buy:
\[ Q + 5 = \frac{240}{\frac{3x}{4}} = \frac{240 \times 4}{3x} = \frac{960}{3x} \]

### Step 3: Create the equation based on the quantities
From the information given, we can set up the following equation:
\[ \frac{960}{3x} = \frac{240}{x} + 5 \]

### Step 4: Clear the fractions by multiplying through by \( 3x \)
To eliminate the denominators, multiply the entire equation by \( 3x \):
\[ 960 = 720 + 15x \]

### Step 5: Solve for \( x \)
Rearranging the equation gives:
\[ 960 - 720 = 15x \]
\[ 240 = 15x \]
\[ x = \frac{240}{15} = 16 \]

### Conclusion
The original price of rice was Rs. 16 per kg.