We are given a 25-litre mixture of milk and water, where the ratio of milk to water is $3:2$. We need to find how many litres of water should be added so that the final mixture contains 50% water.

Step-by-Step Solution:

1. Find the current amount of milk and water in the mixture:

   • Total volume of the mixture = 25 litres.

   • Ratio of milk to water = $3:2$, so the fraction of milk is $\frac{3}{5}$ and the fraction of water is $\frac{2}{5}$.

   • Amount of milk = $\frac{3}{5} \times 25 = 15$ litres.

   • Amount of water = $\frac{2}{5} \times 25 = 10$ litres.

2. Let the amount of water to be added be $x$ litres.

   • After adding $x$ litres of water, the new amount of water becomes $10 + x$ litres.
   • The total volume of the new mixture becomes $25 + x$ litres.

3. Set up the equation for 50% water in the new mixture:

   • For the resultant mixture to have 50% water, the amount of water should be half of the total volume of the mixture.

   $\frac{10 + x}{25 + x} = 0.5$

4. Solve the equation: $10 + x = 0.5 \times (25 + x)$ $10 + x = 12.5 + 0.5x$ $x - 0.5x = 12.5 - 10$ $0.5x = 2.5$ $x = \frac{2.5}{0.5} = 5$

Final Answer:

You need to add 5 litres of water to the mixture so that the resultant mixture has 50% water.

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Would you like further clarification or additional details on any step? Here are some related questions you might find interesting:

1. What if the original ratio of milk to water was different, say 4:1?
2. How many litres of water should be added to make the mixture 40% water instead of 50%?
3. What would happen if we added milk instead of water to the mixture? How would the ratio change?
4. How can you determine the percentage of water in any mixture if given its ratio?
5. Can you create an equation to represent the percentage of a liquid in a mixture based on its initial ratio?

Tip: Always check if the units and percentages in your mixture problems add up correctly to avoid errors!