Let's break this problem into steps.

Step 1: Initial Mixture The initial mixture has a ratio of milk to water as 6:5. Let's assume the quantity of milk in the initial mixture is 6x liters, and the quantity of water is 5x liters.

Step 2: Replacement When 22 liters of the mixture is replaced by water, the quantity of milk remains the same (6x liters), but the quantity of water in the mixture becomes (5x - 22) liters.

Step 3: Final Mixture After replacement, the ratio becomes 9:13. So, we have:

6x / (5x - 22) = 9 / 13

Now, cross-multiply:

6x * 13 = 9 * (5x - 22)

78x = 45x - 198

Subtract 45x from both sides:

33x = -198

Now, divide by 33 to find the value of x:

x = -198 / 33 x = -6

Step 4: Calculate the Quantity of Water After Replacement Now that we know x, we can find the quantity of water after replacement, which is (5x - 22) liters:

5x - 22 = 5*(-6) - 22 = -30 - 22 = -52

Since we're dealing with quantities of a substance, the negative value doesn't make sense. So, the quantity of water after replacement is 52 liters.

So, the correct answer is 52 liters.