A milkman brings 100 litres pure milk from a dairy farmer and he sells 10 litres of it to the first customer, then he refills his vessel by adding 10 litres water. After this, he proceeds to the next house and sells 10 litres of it to the second customer and then he refills his vessel again by adding 10 litres of water. Thus every time he sells 10 litres of milk-pure or impure - he keeps on replacing it with 10 litres of pure water.
Maximum how many customers can get at least 50% milk in the mixture that they purchase from this milkman?

Options

A. 5
B. 6
C. 7
D. None of these

Answer

To solve the problem, we need to determine how many customers can receive at least 50% milk in the mixture sold by the milkman. The milkman starts with 100 liters of pure milk and replaces 10 liters of the mixture with water after each sale.

### Step-by-Step Solution:

1. **Initial Setup**:
- The milkman starts with 100 liters of pure milk.
- He sells 10 liters of this milk to the first customer.

2. **First Sale**:
- After selling 10 liters, the remaining milk = 100 - 10 = 90 liters.
- He adds 10 liters of water, so the total volume remains 100 liters, but the composition changes.
- The mixture now consists of 90 liters of milk and 10 liters of water.

3. **Concentration Calculation for First Customer**:
- The concentration of milk for the first customer = (90 liters milk / 100 liters mixture) = 90%.

4. **Second Sale**:
- The milkman sells another 10 liters of the mixture (which now contains 90% milk).
- Amount of milk in the 10 liters sold = 10 * 90% = 9 liters.
- Amount of water in the 10 liters sold = 10 * 10% = 1 liter.
- Remaining milk after the second sale = 90 - 9 = 81 liters.
- Remaining water after the second sale = 10 - 1 = 9 liters.
- He adds 10 liters of water again, so the total volume is still 100 liters.
- New mixture composition: 81 liters of milk and 19 liters of water.

5. **Concentration Calculation for Second Customer**:
- The concentration of milk for the second customer = (81 liters milk / 100 liters mixture) = 81%.

6. **Third Sale**:
- The milkman sells 10 liters of the mixture (81% milk).
- Amount of milk in the 10 liters sold = 10 * 81% = 8.1 liters.
- Remaining milk = 81 - 8.1 = 72.9 liters.
- Remaining water = 19 - 1.9 = 17.1 liters.
- He adds 10 liters of water again, so the new mixture composition is: 72.9 liters of milk and 27.1 liters of water.

7. **Concentration Calculation for Third Customer**:
- The concentration of milk for the third customer = (72.9 liters milk / 100 liters mixture) = 72.9%.

8. **Continuing This Process**:
- Each time he sells 10 liters of the mixture, the amount of milk decreases by 10% of the remaining milk in the mixture.
- This pattern continues, and we can summarize the remaining milk after each sale:
- After 1st customer: 90 liters milk
- After 2nd customer: 81 liters milk
- After 3rd customer: 72.9 liters milk
- After 4th customer: 65.61 liters milk
- After 5th customer: 59.049 liters milk
- After 6th customer: 53.1441 liters milk
- After 7th customer: 47.82969 liters milk

9. **Finding the Maximum Customers with At Least 50% Milk**:
- The concentration of milk for the sixth customer is approximately 53.14%, which is above 50%.
- The concentration of milk for the seventh customer is approximately 47.83%, which is below 50%.
- Therefore, the maximum number of customers who can receive at least 50% milk is **6**.

### Final Answer:
The maximum number of customers that can get at least 50% milk in the mixture is **6**.