A mixture of milk and water weighs 60 litres which contains `10%` water. How much water should be added to it so that water may be `25%`?

Options

A. 10 litres
B. 9 litres
C. 12 litres
D. 15 litres

Answer

To solve the problem, we need to determine how much water should be added to a mixture of milk and water so that the percentage of water in the mixture becomes 25%.

### Step-by-Step Solution:

1. **Identify the initial quantities**:
- The total weight of the mixture is 60 liters.
- The mixture contains 10% water.
- Therefore, the amount of water in the mixture is:
\[ \text{Water} = 10\% \text{ of } 60 = \frac{10}{100} \times 60 = 6 \text{ liters} \]
- The amount of milk in the mixture is:
\[ \text{Milk} = 60 - 6 = 54 \text{ liters} \]

2. **Let \( x \) be the amount of water to be added**:
- After adding \( x \) liters of water, the new total amount of water will be:
\[ \text{New Water} = 6 + x \text{ liters} \]
- The new total volume of the mixture will be:
\[ \text{New Total Volume} = 60 + x \text{ liters} \]

3. **Set up the equation for the new percentage of water**:
- We want the new percentage of water to be 25%. Therefore, we can set up the equation:
\[ \frac{6 + x}{60 + x} = \frac{25}{100} \]

4. **Cross-multiply to solve the equation**:
- Cross-multiplying gives us:
\[ 100(6 + x) = 25(60 + x) \]
- Simplifying this:
\[ 600 + 100x = 1500 + 25x \]

5. **Rearranging the equation**:
- Bringing all terms involving \( x \) to one side and constant terms to the other side:
\[ 100x - 25x = 1500 - 600 \]
\[ 75x = 900 \]

6. **Solving for \( x \)**:
- Dividing both sides by 75:
\[ x = \frac{900}{75} = 12 \]

7. **Conclusion**:
- Therefore, the amount of water that should be added is **12 liters**.