A reduction of 20% in the price of rice enables a customer to purchase 12.5 kg more for Rs. 800. The original price of rice (per kg) is

Options

A. Rs. 14
B. Rs. 16
C. Rs. 12
D. Rs. 15

Answer

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

### Step 1: Define the variables
Let the original price of rice per kg be \( x \) Rs.

### Step 2: Calculate the reduced price
Since there is a reduction of 20%, the new price after the discount will be:
\[ \text{New Price} = x - 0.2x = 0.8x \]

### Step 3: Determine the quantity of rice purchased
At the original price \( x \), the quantity of rice that can be bought for Rs. 800 is:
\[ \text{Quantity at original price} = \frac{800}{x} \]

At the reduced price \( 0.8x \), the quantity of rice that can be bought for Rs. 800 is:
\[ \text{Quantity at reduced price} = \frac{800}{0.8x} = \frac{800}{\frac{4}{5}x} = \frac{800 \times 5}{4x} = \frac{4000}{4x} = \frac{1000}{x} \]

### Step 4: Set up the equation
According to the problem, the difference in the quantity purchased at the reduced price and the original price is 12.5 kg:
\[ \frac{1000}{x} - \frac{800}{x} = 12.5 \]

### Step 5: Simplify the equation
Combining the fractions gives:
\[ \frac{1000 - 800}{x} = 12.5 \]
\[ \frac{200}{x} = 12.5 \]

### Step 6: Solve for \( x \)
To find \( x \), we can cross-multiply:
\[ 200 = 12.5x \]
Now, divide both sides by 12.5:
\[ x = \frac{200}{12.5} = 16 \]

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

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