A reduction of 10% in the price of a commodity enables a person to buy 25 kg more for Rs. 225. The original price of the commodity per kg was

Options

A. Rs. 2
B. Rs. 1
C. Rs. 2.50
D. Rs. 1.50

Answer

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

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

### Step 2: Calculate the reduced price
Since there is a reduction of 10%, the new price after the discount can be calculated as:
\[ \text{Reduced Price} = x - 0.10x = 0.90x \]

### Step 3: Determine the quantity that can be bought at the original price
At the original price \( x \), the quantity that can be bought for Rs. 225 is:
\[ \text{Quantity at original price} = \frac{225}{x} \]

### Step 4: Determine the quantity that can be bought at the reduced price
At the reduced price \( 0.90x \), the quantity that can be bought for Rs. 225 is:
\[ \text{Quantity at reduced price} = \frac{225}{0.90x} \]

### Step 5: Set up the equation
According to the problem, the difference in quantity bought at the reduced price and the original price is 25 kg. Therefore, we can set up the equation:
\[ \frac{225}{0.90x} - \frac{225}{x} = 25 \]

### Step 6: Simplify the equation
To simplify the equation, we can find a common denominator:
\[ \frac{225x - 225 \cdot 0.90x}{0.90x^2} = 25 \]
This simplifies to:
\[ \frac{225x - 202.5x}{0.90x^2} = 25 \]
\[ \frac{22.5x}{0.90x^2} = 25 \]

### Step 7: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 22.5x = 25 \cdot 0.90x^2 \]
\[ 22.5x = 22.5x^2 \]

### Step 8: Rearranging the equation
Dividing both sides by 22.5 (assuming \( x \neq 0 \)):
\[ 1 = x \]

### Step 9: Conclusion
Thus, the original price of the commodity per kg is:
\[ x = 10 \text{ Rs.} \]