80 litre mixture of milk and water contains `10%` milk . How much 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 achieve a situation where the water percentage in the mixture is 80%.

### Step 1: Determine the current amount of milk in the mixture.
The mixture is 80 litres and contains 10% milk.

\[ \text{Amount of milk} = 10\% \text{ of } 80 \text{ litres} = \frac{10}{100} \times 80 = 8 \text{ litres} \]

### Step 2: Determine the current amount of water in the mixture.
Since the total mixture is 80 litres and we have found that there are 8 litres of milk, we can find the amount of water.

\[ \text{Amount of water} = \text{Total mixture} - \text{Amount of milk} = 80 - 8 = 72 \text{ litres} \]

### Step 3: Set up the equation to find the amount of milk to be added.
Let \( x \) be the amount of milk that we need to add. After adding \( x \) litres of milk, the new total amount of milk will be \( 8 + x \) litres, and the total volume of the mixture will be \( 80 + x \) litres.

We want the percentage of water in the new mixture to be 80%. Therefore, the percentage of milk in the new mixture will be 20% (since 100% - 80% = 20%).

\[ \frac{\text{Amount of milk}}{\text{Total mixture}} = 20\% \]

This can be expressed as:

\[ \frac{8 + x}{80 + x} = \frac{20}{100} \]

### Step 4: Solve the equation.
Cross-multiplying gives us:

\[ 100(8 + x) = 20(80 + x) \]

Expanding both sides:

\[ 800 + 100x = 1600 + 20x \]

Rearranging the equation to isolate \( x \):

\[ 100x - 20x = 1600 - 800 \]
\[ 80x = 800 \]
\[ x = \frac{800}{80} = 10 \]

### Conclusion:
The amount of milk that must be added to the mixture is \( 10 \) litres.

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