A milkman purchases the milk at Rs x per liter and sells it at Rs 2x per liter and still he mixes 2 liter water with every 6 liter of pure milk. What is the profit percentage?

Answer

To find the profit percentage for the milkman, we can break down the problem step by step.

### Step 1: Determine the Cost Price (CP) of Milk
The milkman purchases milk at Rs. x per liter.

### Step 2: Calculate the Total Cost Price for Milk
He mixes 6 liters of pure milk with 2 liters of water. The cost of water is Rs. 0, so we only need to consider the cost of the milk.
- Cost of 6 liters of milk = 6 liters × Rs. x/liter = Rs. 6x

### Step 3: Calculate the Selling Price (SP) of the Mixture
The milkman sells the mixture (6 liters of milk + 2 liters of water = 8 liters total) at Rs. 2x per liter.
- Selling Price of 8 liters = 8 liters × Rs. 2x/liter = Rs. 16x

### Step 4: Calculate the Profit
Profit is calculated as the Selling Price minus the Cost Price.
- Profit = Selling Price - Cost Price
- Profit = Rs. 16x - Rs. 6x = Rs. 10x

### Step 5: Calculate the Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
- Cost Price of 8 liters = Rs. 6x
- Profit Percentage = \(\left(\frac{10x}{6x}\right) \times 100\)

### Step 6: Simplify the Profit Percentage
- Profit Percentage = \(\left(\frac{10}{6}\right) \times 100 = \frac{500}{3} \approx 166.67\%\)

### Final Answer
The profit percentage is approximately **166.67%**.

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