A reduction of `20%` in the price of sugar enables a housewife to purchase 6 kg more for ₹ 240. What is the original price per kg of sugar?

Options

A. ₹ 10 per kg
B. ₹ 8 per kg
C. ₹ 6per kg
D. ₹ 5 per kg

Answer

To solve the problem step by step, we need to find the original price per kg of sugar based on the information provided.

### Step-by-Step Solution:

1. **Understanding the Reduction in Price**:
- The price of sugar is reduced by 20%. This means the new price is 80% of the original price.
- If we denote the original price per kg of sugar as \( P \), then the new price after the reduction is:
\[ \text{New Price} = P - 0.20P = 0.80P \]

2. **Calculating the Quantity of Sugar Purchased**:
- According to the problem, the housewife can buy 6 kg more sugar for ₹240 after the price reduction.
- Let’s denote the quantity of sugar she could buy at the original price as \( Q \) kg. Therefore, at the original price, the amount of sugar she could buy for ₹240 is:
\[ Q = \frac{240}{P} \]
- After the price reduction, the quantity of sugar she can buy for the same amount (₹240) is:
\[ Q + 6 = \frac{240}{0.80P} \]

3. **Setting Up the Equation**:
- We can set up the equation based on the quantities:
\[ \frac{240}{0.80P} = \frac{240}{P} + 6 \]

4. **Simplifying the Equation**:
- To eliminate the fractions, we can multiply through by \( 0.80P \):
\[ 240 = 240 + 6 \cdot 0.80P \]
- Simplifying this gives:
\[ 0 = 6 \cdot 0.80P \]
- This simplifies to:
\[ 0 = 4.8P \]
- Rearranging gives:
\[ 4.8P = 240 - 240 \]
- Thus, we have:
\[ 6 = \frac{240}{P} - \frac{240}{0.80P} \]

5. **Finding \( P \)**:
- Rearranging the equation gives:
\[ 6 = \frac{240(0.80 - 1)}{0.80P} \]
- This leads to:
\[ 6 = \frac{-240 \cdot 0.20}{0.80P} \]
- Cross-multiplying gives:
\[ 6 \cdot 0.80P = -240 \cdot 0.20 \]
- Solving for \( P \):
\[ P = \frac{-240 \cdot 0.20}{6 \cdot 0.80} \]
- Simplifying gives:
\[ P = \frac{240 \cdot 0.20}{4.8} = 10 \]

6. **Conclusion**:
- The original price per kg of sugar is ₹10.