In a mixture of milk and water, 20% of the mixture is replaced with half as much water, therefore increasing the quantity of water in the mixture by 40%. If the final mixture contains 60 liters of milk, find the quantity (in liters) of water in it.

To solve this problem, let's follow a step-by-step approach:

### Step 1: Define the initial quantities
Let the initial amount of the mixture be \( M \) liters.  
Let the initial amount of water be \( W \) liters.  
Let the initial amount of milk be \( M - W \) liters.

### Step 2: Replacement process
According to the problem, 20% of the mixture is replaced with half as much water.

The amount of mixture removed is \( 0.2M \) liters.  
This \( 0.2M \) liters of mixture contains \( 0.2W \) liters of water and \( 0.2(M - W) \) liters of milk.

The quantity of water removed is \( 0.2W \) liters.  
The quantity of milk removed is \( 0.2(M - W) \) liters.

This removed mixture is replaced with half as much water. So, the amount of water added is \( \frac{0.2M}{2} = 0.1M \) liters.

### Step 3: New quantity of water after replacement
The new quantity of water, \( W_{\text{new}} \), is given by:
\[
W_{\text{new}} = W - 0.2W + 0.1M = 0.8W + 0.1M
\]
We are given that this new quantity of water is 40% more than the original quantity of water, so:
\[
W_{\text{new}} = W + 0.4W = 1.4W
\]
Thus, we have:
\[
1.4W = 0.8W + 0.1M
\]
\[
0.6W = 0.1M
\]
\[
W = \frac{0.1M}{0.6} = \frac{M}{6}
\]

### Step 4: Use the information about the amount of milk
The final amount of milk in the mixture is given as 60 liters. Since 20% of the milk was removed and the remainder was \( 0.8 \times \) the original amount, we have:
\[
\text{Final amount of milk} = 0.8(M - W) = 60 \text{ liters}
\]
\[
M - W = \frac{60}{0.8} = 75 \text{ liters}
\]
We already know \( W = \frac{M}{6} \), so:
\[
M - \frac{M}{6} = 75
\]
\[
\frac{5M}{6} = 75
\]
\[
M = \frac{75 \times 6}{5} = 90 \text{ liters}
\]

### Step 5: Calculate the quantity of water
Substitute \( M = 90 \) liters into \( W = \frac{M}{6} \):
\[
W = \frac{90}{6} = 15 \text{ liters}
\]

Thus, the quantity of water in the final mixture is **15 liters**.

### Summary
- **Quantity of water in the final mixture:** 15 liters.

Would you like more details, or do you have any questions?

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Here are 5 related questions to deepen your understanding:
1. What would happen if the initial mixture had a different ratio of milk to water?
2. How would the result change if 30% of the mixture was replaced instead of 20%?
3. Can you determine the final percentage of water in the mixture?
4. What if the replacement was done with more water instead of half as much?
5. How would the problem change if the final milk content was different?

**Tip:** Always double-check the assumptions you make when setting up equations in word problems.

Explore how to solve a complex problem involving the replacement of a milk and water mixture, increasing water content by 40%. Learn the step-by-step solution to find the quantity of water in the final mixture. Suitable for Grades 9-12.

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