Preeti bought `8 1/2` — kg of sugar for Rs `242 1/4`. Find the price of sugar per kg.

Answer

To find the price of sugar per kg, we will follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
1. **Convert `8 1/2` kg of sugar to an improper fraction:**
- \( 8 \frac{1}{2} = \frac{(8 \times 2) + 1}{2} = \frac{16 + 1}{2} = \frac{17}{2} \) kg

2. **Convert `242 1/4` rupees to an improper fraction:**
- \( 242 \frac{1}{4} = \frac{(242 \times 4) + 1}{4} = \frac{968 + 1}{4} = \frac{969}{4} \) rupees

### Step 2: Calculate the price per kg
3. **Set up the equation for the price per kg:**
- Price per kg = Total cost / Total weight
- Price per kg = \( \frac{969/4}{17/2} \)

4. **Dividing the fractions:**
- To divide by a fraction, multiply by its reciprocal:
- \( \frac{969}{4} \div \frac{17}{2} = \frac{969}{4} \times \frac{2}{17} \)

5. **Multiply the fractions:**
- \( = \frac{969 \times 2}{4 \times 17} = \frac{1938}{68} \)

### Step 3: Simplify the fraction
6. **Simplify \( \frac{1938}{68} \):**
- Find the greatest common divisor (GCD) of 1938 and 68.
- The GCD is 34.
- \( \frac{1938 \div 34}{68 \div 34} = \frac{57}{2} \)

### Step 4: Convert to a decimal or mixed number
7. **Convert \( \frac{57}{2} \) to a decimal:**
- \( \frac{57}{2} = 28.5 \)

### Final Answer
The price of sugar per kg is Rs 28.5.

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