In a 50 litre mixture of water and milk, water is only `20%.` The milkman gives 10 liters of this mixture to a customer and then he adds up 10 liters of pure water in the remaining mixture. The percenatge of water in the final mixture is :

Options

A. `84%`
B. `74%`
C. `26%`
D. `36%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the initial amount of water and milk in the mixture.
- The total volume of the mixture is 50 liters.
- Water constitutes 20% of the mixture.

\[ \text{Amount of water} = 20\% \text{ of } 50 \text{ liters} = \frac{20}{100} \times 50 = 10 \text{ liters} \]

- Therefore, the amount of milk in the mixture is:

\[ \text{Amount of milk} = 50 \text{ liters} - 10 \text{ liters} = 40 \text{ liters} \]

### Step 2: Calculate the remaining mixture after giving 10 liters to the customer.
- The milkman gives away 10 liters of the mixture. Thus, the remaining mixture is:

\[ \text{Remaining mixture} = 50 \text{ liters} - 10 \text{ liters} = 40 \text{ liters} \]

### Step 3: Determine the amount of water and milk in the remaining 40 liters.
- Since the mixture is uniform, the ratio of water and milk remains the same in the 10 liters given away.

- The amount of water in the 10 liters given away is:

\[ \text{Water in 10 liters} = 20\% \text{ of } 10 \text{ liters} = \frac{20}{100} \times 10 = 2 \text{ liters} \]

- Therefore, the amount of water left in the remaining 40 liters is:

\[ \text{Remaining water} = 10 \text{ liters} - 2 \text{ liters} = 8 \text{ liters} \]

- The amount of milk left in the remaining 40 liters is:

\[ \text{Remaining milk} = 40 \text{ liters} - 8 \text{ liters} = 32 \text{ liters} \]

### Step 4: Add 10 liters of pure water to the remaining mixture.
- After giving away the mixture, the milkman adds 10 liters of pure water to the remaining mixture.

- Thus, the total amount of water after adding the pure water is:

\[ \text{Total water} = 8 \text{ liters} + 10 \text{ liters} = 18 \text{ liters} \]

### Step 5: Calculate the total volume of the final mixture.
- The total volume of the final mixture is:

\[ \text{Total final mixture} = 40 \text{ liters} + 10 \text{ liters} = 50 \text{ liters} \]

### Step 6: Calculate the percentage of water in the final mixture.
- The percentage of water in the final mixture is calculated as follows:

\[ \text{Percentage of water} = \left( \frac{\text{Total water}}{\text{Total final mixture}} \right) \times 100 = \left( \frac{18 \text{ liters}}{50 \text{ liters}} \right) \times 100 = 36\% \]

### Final Answer:
The percentage of water in the final mixture is **36%**.

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