In a mixture , the ratio of the milk and water is 6: 5 . when 22 liter mixture is replaced by water, the ratio becomes 9 : 13. Find the quantity o water after replacement .

Let M represent the amount of milk and W represent the amount of water in the original mixture.

Given that the ratio of milk to water is 6:5, we can write:

M/W = 6/5

Now, let's consider the replacement. When 22 liters of the mixture are replaced by water, the total amount of milk remains the same, but the total amount of the mixture decreases by 22 liters.

So, after replacement, the new ratio of milk to water becomes 9:13, which we can write as:

(M - 22) / (W + 22) = 9/13

Now, we have a system of two equations:

1. M/W = 6/5
2. (M - 22) / (W + 22) = 9/13

We can solve this system of equations to find the values of M and W.

First, let's solve equation 1 for M:

M = (6/5)W

Now, substitute this expression for M into equation 2:

((6/5)W - 22) / (W + 22) = 9/13

Cross-multiply:

13(6W - 22) = 9(5W + 22)

Expand and simplify:

78W - 286 = 45W + 198

Subtract 45W from both sides:

33W - 286 = 198

Add 286 to both sides:

33W = 484

Now, divide by 33:

W = 484 / 33 W = 52/3

So, the amount of water in the original mixture is 52/3 liters.

Now, to find the amount of water after replacement, add 22 liters to it:

Water after replacement = (52/3) + 22 Water after replacement = 52/3 + 66/3 Water after replacement = 118/3 liters

So, the quantity of water after replacement is 118/3 liters, which is equivalent to 52 liters (rounded to the nearest whole number). Therefore, the answer is 52 liters.