80 litre mixture of milk and water contains 10% milk. How mach milk (in litres) must be added to make water percentage in the mixture as 80%?

Options

A. 8
B. 9
C. 10
D. 12

Answer

To solve the problem step by step, we need to determine how much milk must be added to an 80-litre mixture that currently contains 10% milk, in order to make the percentage of water in the mixture 80%.

### Step 1: Calculate the initial amount of milk and water in the mixture.
The mixture is 80 litres and contains 10% milk.

- Amount of milk = 10% of 80 litres = \( \frac{10}{100} \times 80 = 8 \) litres
- Amount of water = 80 litres - Amount of milk = \( 80 - 8 = 72 \) litres

### Step 2: Set up the equation for the final mixture.
We want the final mixture to have 80% water. If we add \( x \) litres of milk, the total volume of the mixture will be \( 80 + x \) litres.

To have 80% water in the final mixture:
- Amount of water = 80% of total volume = \( 0.8 \times (80 + x) \)
- Amount of milk = 20% of total volume = \( 0.2 \times (80 + x) \)

### Step 3: Set up the equation for the amount of milk.
The amount of milk in the final mixture will be the initial amount of milk plus the amount of milk added:
- Initial milk = 8 litres
- Added milk = \( x \) litres
- Total milk = \( 8 + x \)

From the previous step, we know that the total milk must equal 20% of the total volume:
\[ 8 + x = 0.2 \times (80 + x) \]

### Step 4: Solve the equation.
Now, we will solve the equation:
\[ 8 + x = 0.2 \times (80 + x) \]
\[ 8 + x = 16 + 0.2x \]
Now, rearranging the equation:
\[ x - 0.2x = 16 - 8 \]
\[ 0.8x = 8 \]
\[ x = \frac{8}{0.8} = 10 \]

### Conclusion:
The amount of milk that must be added is **10 litres**.