Vessel A contains 150 liters mixture of milk and water in which water is 40%. ‘x’ liters mixture is taken out (quantity of water in ‘x’ liters is 12 liters) and poured into vessel B which already contain ‘x’ liters water . Find the difference between quantity (in liters) of milk and water in resultant mixture of vessel B.

To find the difference between the quantity of milk and water in the resultant mixture of vessel B, we can break down the problem step-by-step.

Step 1: Determine the composition of the mixture in Vessel A.
Vessel A contains 150 liters of a mixture of milk and water.
Water percentage in Vessel A = 40%
Therefore, the percentage of milk in Vessel A = 100% - 40% = 60%.
The ratio of milk to water in Vessel A is:
Milk : Water = 60% : 40% = 3 : 2

Step 2: Find the value of 'x' using the taken-out mixture.
When a quantity of 'x' liters of the mixture is taken out of Vessel A, the ratio of milk to water in this extracted quantity 'x' remains the same as in Vessel A, which is 3 : 2.
Let the quantity of milk and water in 'x' liters be 3k and 2k respectively, where k is a constant.
We are given that the quantity of water in 'x' liters is 12 liters.
$2k=12$
$k=6$
Now we can find the quantity of milk in 'x' liters:
Milk in 'x' liters = 3k = 3 × 6 = 18 liters.
The total quantity 'x' taken out is:
$x=\text{Milk}+\text{Water}=18+12=30\text{liters}$

Step 3: Analyze the composition of the resultant mixture in Vessel B.
The 'x' liters of mixture taken out (which contains 18 liters of milk and 12 liters of water) is poured into Vessel B.
Vessel B already contains 'x' liters of pure water.
Since $x=30$, Vessel B initially contains 30 liters of water.
After pouring the 'x' liters of mixture into Vessel B:
Total quantity of milk in Vessel B = Milk from 'x' = 18 liters.
Total quantity of water in Vessel B = Initial water in B + Water from 'x' = 30 + 12 = 42 liters.

Step 4: Find the difference between the quantity of milk and water in Vessel B.
Difference = Quantity of water - Quantity of milk
$\text{Difference}=42-18=24\text{liters}$

Thus, the difference between the quantity of milk and water in the resultant mixture of vessel B is 24 liters.