A mixture of water and milk contains 80% milk. In 50 litre 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 the above

Answer

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

### Step 1: Understand the Initial Mixture
The mixture consists of 80% milk and 20% water. Given that the total volume of the mixture is 50 liters, we can calculate the amount of milk and water in the mixture.

- **Amount of milk** = 80% of 50 liters = \( \frac{80}{100} \times 50 = 40 \) liters
- **Amount of water** = 20% of 50 liters = \( \frac{20}{100} \times 50 = 10 \) liters

### Step 2: Set Up the Desired Condition
We want to increase the percentage of water in the mixture to 50%. This means that the amount of water should equal the amount of milk in the new mixture.

Let \( x \) be the amount of water we need to add.

### Step 3: Write the Equation
After adding \( x \) liters of water, the total amount of water will be \( 10 + x \) liters, and the total volume of the mixture will be \( 50 + x \) liters.

To achieve 50% water in the new mixture, we set up the equation:

\[ \frac{10 + x}{50 + x} = 0.5 \]

### Step 4: Solve the Equation
Now, we will solve for \( x \):

1. Cross-multiply:
\[ 10 + x = 0.5(50 + x) \]

2. Distribute the 0.5:
\[ 10 + x = 25 + 0.5x \]

3. Rearrange the equation:
\[ x - 0.5x = 25 - 10 \]
\[ 0.5x = 15 \]

4. Divide both sides by 0.5:
\[ x = \frac{15}{0.5} = 30 \]

### Step 5: Conclusion
Thus, the amount of water required to increase the percentage of water to 50% is **30 liters**.

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