Introduction:
The problem requires us to find the ratio in which two solutions with different milk-water ratios must be mixed to obtain a resultant solution with a different milk-water ratio.

Given Information:
Solution 1 - Milk:Water = 2:3
Solution 2 - Milk:Water = 4:5
Resultant Solution - Milk:Water = 3:4

Assumptions:
Let's assume that we have x liters of Solution 1 and y liters of Solution 2.

Solving the Problem:
We need to find the ratio in which Solutions 1 and 2 should be mixed to obtain the desired milk-water ratio.

Step 1: Calculate Milk and Water Content of Solutions 1 and 2
- Solution 1: Milk = 2x/5, Water = 3x/5
- Solution 2: Milk = 4y/9, Water = 5y/9

Step 2: Calculate Milk and Water Content of Resultant Solution
- Resultant Solution: Milk = (2x/5 + 4y/9), Water = (3x/5 + 5y/9)

Step 3: Apply the Conditions of the Problem
- Milk:Water = 3:4
- Therefore, (2x/5 + 4y/9)/(3x/5 + 5y/9) = 3/4

Step 4: Solve the Equation Obtained in Step 3
- 8x + 12y = 27x + 45y
- 19x = 33y
- x/y = 33/19

Answer:
- Solutions 1 and 2 should be mixed in the ratio of 33:19 to obtain a resultant solution with a milk-water ratio of 3:4.

Explanation:
- We calculated the milk and water content of Solutions 1 and 2 using the given milk-water ratios and the assumption of x and y liters.
- We then calculated the milk and water content of the resultant solution by adding the milk and water content of Solutions 1 and 2.
- We applied the condition of the desired milk-water ratio and obtained an equation relating x and y.
- Solving the equation gave us the required ratio in which Solutions 1 and 2 should be mixed.
- Therefore, the answer is a ratio of 33:19.

Solution-1
Milk:Water = 2:3(2x+3x=5x)
Solution-2
Milk:Water = 4:5(4y+5y=9y)

Convert each solution into equal parts
Solution-1
Milk:Water = 9×(2:3)= 18:27(18x+27x=45x)
Solution-2
Milk:Water = 5×(4:5)= 20:25(20y+25y=45y)
Now we need to find x:y(?)
Given that,
(18x+20y):(27x+25y)=3:4
solving we get, x:y=5:9
Answer is 5:9