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 will follow these calculations:

**Step 1: Determine the amount of milk in the initial mixture.**
- The total volume of the mixture is 80 liters.
- The percentage of milk in the mixture is 10%.
- Therefore, the amount of milk in the mixture is:
\[ \text{Amount of milk} = \frac{10}{100} \times 80 = 8 \text{ liters} \]

**Step 2: Determine the amount of water in the initial mixture.**
- Since the total mixture is 80 liters and we have 8 liters of milk, the amount of water is:
\[ \text{Amount of water} = 80 - 8 = 72 \text{ liters} \]

**Step 3: Set up the equation to find the amount of milk to be added.**
- Let \( x \) be the amount of milk to be added.
- After adding \( x \) liters of milk, the new amount of milk will be \( 8 + x \) liters.
- The total volume of the mixture will then be \( 80 + x \) liters.

**Step 4: Set up the equation for the percentage of water in the new mixture.**
- We want the percentage of water in the new mixture to be 80%.
- The amount of water remains 72 liters.
- Therefore, we can set up the equation:
\[ \frac{\text{Amount of water}}{\text{Total mixture}} = 80\% \]
\[ \frac{72}{80 + x} = \frac{80}{100} \]

**Step 5: Cross-multiply to solve for \( x \).**
- Cross-multiplying gives us:
\[ 72 \times 100 = 80 \times (80 + x) \]
\[ 7200 = 6400 + 80x \]
\[ 7200 - 6400 = 80x \]
\[ 800 = 80x \]
\[ x = \frac{800}{80} = 10 \]

**Step 6: Conclusion.**
- The amount of milk that must be added to make the water percentage in the mixture 80% is **10 liters**.

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