A 120 litre mixture of milk and water contains 40% milk. How much milk (in litres) must be add ed so that milk becomes 50%?

Options

A. 28
B. 30
C. 24
D. 32

Answer

To solve the problem step by step, we need to determine how much milk must be added to a 120-liter mixture that currently contains 40% milk, so that the final mixture contains 50% milk.

### Step 1: Determine the current amount of milk in the mixture.
The mixture is 120 liters and contains 40% milk.

\[ \text{Amount of milk} = 40\% \text{ of } 120 \text{ liters} = \frac{40}{100} \times 120 = 48 \text{ liters} \]

### Step 2: Determine the current amount of water in the mixture.
Since the mixture is 120 liters and contains 40% milk, the remaining percentage is water.

\[ \text{Amount of water} = 120 \text{ liters} - 48 \text{ liters} = 72 \text{ liters} \]

### Step 3: Set up the equation for the new mixture.
Let \( x \) be the amount of milk to be added. After adding \( x \) liters of milk, the total amount of milk will be \( 48 + x \) liters, and the total volume of the mixture will be \( 120 + x \) liters.

We want the new mixture to contain 50% milk, so we can set up the equation:

\[ \frac{48 + x}{120 + x} = 50\% \]

### Step 4: Convert the percentage to a fraction and solve for \( x \).
Converting 50% to a fraction gives us \( \frac{1}{2} \). Now we can rewrite the equation:

\[ \frac{48 + x}{120 + x} = \frac{1}{2} \]

Cross-multiplying gives:

\[ 2(48 + x) = 1(120 + x) \]

Expanding both sides:

\[ 96 + 2x = 120 + x \]

### Step 5: Solve for \( x \).
Rearranging the equation to isolate \( x \):

\[ 2x - x = 120 - 96 \]

\[ x = 24 \]

### Conclusion:
Thus, the amount of milk that must be added to the mixture is **24 liters**.

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