A reduction of 15% in the price of rice enables a purchaser to obtain 3 kg more for Rs 150. The reduced price per kg is ______

Options

A. Rs 8.50
B. Rs 9
C. Rs 10
D. Rs 7.50

Answer

To solve the problem step by step, let's break it down:

**Step 1: Understand the problem**
We know that a reduction of 15% in the price of rice allows a purchaser to buy 3 kg more rice for Rs 150. We need to find the reduced price per kg of rice.

**Step 2: Let the original price per kg be 'x'**
Let the original price of rice per kg be \( x \) rupees.

**Step 3: Calculate the reduced price**
Since there is a reduction of 15%, the reduced price per kg will be:
\[ \text{Reduced Price} = x - 0.15x = 0.85x \]

**Step 4: Determine the quantity of rice purchased at the original price**
At the original price \( x \), the quantity of rice that can be bought for Rs 150 is:
\[ \text{Quantity at original price} = \frac{150}{x} \]

**Step 5: Determine the quantity of rice purchased at the reduced price**
At the reduced price \( 0.85x \), the quantity of rice that can be bought for Rs 150 is:
\[ \text{Quantity at reduced price} = \frac{150}{0.85x} \]

**Step 6: Set up the equation based on the information given**
According to the problem, the difference in quantity purchased at the reduced price and the original price is 3 kg:
\[ \frac{150}{0.85x} - \frac{150}{x} = 3 \]

**Step 7: Solve the equation**
To solve this equation, we can find a common denominator:
\[ 150 \left( \frac{x - 0.85x}{0.85x^2} \right) = 3 \]
This simplifies to:
\[ 150 \left( \frac{0.15x}{0.85x^2} \right) = 3 \]
Now, simplifying further:
\[ \frac{150 \times 0.15}{0.85} = 3x \]
\[ \frac{22.5}{0.85} = 3x \]
\[ 22.5 = 3x \times 0.85 \]
\[ 22.5 = 2.55x \]
\[ x = \frac{22.5}{2.55} \approx 8.82 \text{ (original price per kg)} \]

**Step 8: Calculate the reduced price**
Now, we can find the reduced price:
\[ \text{Reduced Price} = 0.85x = 0.85 \times 8.82 \approx 7.49 \]

Thus, the reduced price per kg is approximately Rs 7.49.

### Final Answer:
The reduced price per kg is Rs 7.49.