In a 50 litre mixture of water and milk, water is only 20%. The milkman gives 10 litre of this mixture to a customer and then he adds up 10 litres of pure water in the remaining mixture. The percentage 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: Calculate the initial amount of water and milk in the mixture
The total mixture is 50 liters, and water constitutes 20% of this mixture.

- Amount of water = 20% of 50 liters
- Amount of milk = Total mixture - Amount of water

**Calculations:**
- Amount of water = (20/100) * 50 = 10 liters
- Amount of milk = 50 - 10 = 40 liters

### Step 2: Determine the amount of water in the 10 liters of mixture given to the customer
The milkman gives away 10 liters of the mixture. We need to find out how much water is in this 10 liters.

The ratio of water to milk in the original mixture is 1:4 (10 liters of water and 40 liters of milk).

- Amount of water in 10 liters of mixture = (1/5) * 10 liters = 2 liters

### Step 3: Calculate the remaining amount of water and milk after giving away the mixture
After giving away 10 liters of the mixture, we need to find the remaining amounts of water and milk.

- Remaining water = Initial water - Water given away
- Remaining milk = Initial milk - Milk given away

**Calculations:**
- Remaining water = 10 liters - 2 liters = 8 liters
- Remaining milk = 40 liters - (10 liters - 2 liters) = 40 liters - 8 liters = 32 liters

### Step 4: Add 10 liters of pure water to the remaining mixture
Now, the milkman adds 10 liters of pure water to the remaining mixture.

- New amount of water = Remaining water + Added water
- New amount of milk = Remaining milk (remains unchanged)

**Calculations:**
- New amount of water = 8 liters + 10 liters = 18 liters
- New amount of milk = 32 liters

### Step 5: Calculate the total volume of the final mixture
The total volume of the final mixture is the sum of the new amounts of water and milk.

**Calculations:**
- Total mixture = New amount of water + New amount of milk
- Total mixture = 18 liters + 32 liters = 50 liters

### Step 6: Calculate the percentage of water in the final mixture
Now we can find the percentage of water in the final mixture.

**Calculations:**
- Percentage of water = (Amount of water / Total mixture) * 100
- Percentage of water = (18 liters / 50 liters) * 100 = 36%

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

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