A mixture of water and milk contains 80% milk. In 50 litres of such a mixture, how many litres of water is required to increase the percentage of water to, 50%?

Options

A. 20
B. 15
C. 30
D. none of these

Answer

To solve the problem step by step, we need to determine how much water is required to increase the percentage of water in a mixture of water and milk from 20% to 50%.

### Step 1: Determine the current composition of the mixture.
The mixture consists of 50 liters, with 80% being milk.

- **Calculation**:
- Amount of milk = 80% of 50 liters = (80/100) * 50 = 40 liters
- Amount of water = Total mixture - Amount of milk = 50 liters - 40 liters = 10 liters

### Step 2: Set up the new ratio for the desired percentage.
We want to increase the percentage of water to 50%. This means that in the new mixture, water should be equal to milk.

- **Understanding the new ratio**:
- If water is to be 50% of the total mixture, then water = milk.
- Therefore, the new ratio of water to milk should be 1:1.

### Step 3: Determine the amount of water needed to achieve the new ratio.
Let \( x \) be the amount of water we need to add. After adding \( x \) liters of water, the total amount of water will be \( 10 + x \) liters, and the amount of milk will still be 40 liters.

- **Setting up the equation**:
- Total mixture after adding water = 50 + \( x \) liters
- We want the amount of water to equal the amount of milk:

\[ 10 + x = 40 \]

### Step 4: Solve for \( x \).
- **Calculation**:
\[ x = 40 - 10 = 30 \text{ liters} \]

### Conclusion:
To increase the percentage of water in the mixture to 50%, we need to add **30 liters of water**.

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