A milkman mixes `10%` water in pure milk but he is not content with it so, he again mixes `10%` more water in the previous mixture. What is the profit percentage of milkman if he sells it at cost price:

Options

A. `11.11%`
B. `20%`
C. `21%`
D. `12.1%`

Answer

To solve the problem step-by-step, we need to analyze the situation where the milkman mixes water with pure milk twice, each time adding 10% water to the previous mixture.

### Step 1: Understand the Initial Mixture
Let’s assume the cost of pure milk is `100` (this represents the cost price of 1 liter of pure milk).

### Step 2: First Mixture
When the milkman adds `10%` water to the pure milk:
- Amount of pure milk = 100
- Amount of water added = 10% of 100 = 10
- Total mixture = 100 + 10 = 110

### Step 3: Calculate the Cost Price of the First Mixture
The cost price of the first mixture remains the same as the cost of pure milk, which is `100`.

### Step 4: Second Mixture
Now, the milkman adds `10%` water to the first mixture:
- Amount of the first mixture = 110
- Amount of water added = 10% of 110 = 11
- Total mixture after the second addition = 110 + 11 = 121

### Step 5: Calculate the Total Cost of the Second Mixture
The cost price of the second mixture is still based on the cost of pure milk, which is `100`.

### Step 6: Calculate the Amount of Pure Milk in the Final Mixture
In the final mixture of `121`, the amount of pure milk is:
- Pure milk from the first mixture = 100
- Pure milk from the second mixture = 100 (remains unchanged)

### Step 7: Calculate the Total Amount of Water in the Final Mixture
The total amount of water in the final mixture is:
- Water from the first mixture = 10
- Water from the second mixture = 11
- Total water = 10 + 11 = 21

### Step 8: Calculate the Percentage of Pure Milk in the Final Mixture
The percentage of pure milk in the final mixture is:
- Pure milk = 100
- Total mixture = 121
- Percentage of pure milk = (100 / 121) * 100 ≈ 82.64%

### Step 9: Calculate the Selling Price
The milkman sells the final mixture at the cost price of pure milk, which is `100`.

### Step 10: Calculate the Profit
The profit is calculated based on the amount of pure milk he is selling:
- Selling price of pure milk = 100
- Cost price of the mixture = 100
- Profit = Selling Price - Cost Price = 100 - (100 * (100 / 121)) = 100 - 82.64 ≈ 17.36

### Step 11: Calculate the Profit Percentage
Profit percentage is calculated as:
- Profit Percentage = (Profit / Cost Price) * 100 = (17.36 / 100) * 100 ≈ 17.36%

### Final Answer
The profit percentage of the milkman is approximately **17.36%**.