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.

Let us break down the problem step-by-step to find the difference between the quantity of milk and water in the resultant mixture of vessel B.

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

Step 2: Analyze the mixture taken out
A quantity of $x$ liters of the mixture is taken out of Vessel A.
Since the mixture is homogeneous, the ratio of milk to water in the $x$ liters removed remains the same as in Vessel A, which is $3:2$.
We are given that the quantity of water in this $x$ liters is 12 liters.
Using the ratio, we can set up the proportion for water:
$\frac{2}{3+2}\times x=12$
$\frac{2}{5}\times x=12$
$x=12\times \frac{5}{2}=30\text{liters}$
So, the total quantity of mixture taken out is $x=30$ liters.
The quantity of milk in these 30 liters is:
$30-12=18\text{liters}$

Step 3: Analyze the composition of Vessel B
The 30 liters mixture (containing 18 liters of milk and 12 liters of water) is poured into Vessel B.
Vessel B already contains $x$ liters of water, which is 30 liters of water.
Now, let us calculate the total quantity of milk and water in Vessel B:
Total milk in Vessel B = 18 liters (from the mixture)
Total water in Vessel B = 12 liters (from the mixture) + 30 liters (already present) = 42 liters

Step 4: Find the difference between milk and water in Vessel B
We need to find the difference between the quantity of milk and water in the resultant mixture of Vessel B:
$\text{Difference}=|\text{Quantity of Water}-\text{Quantity of Milk}|$
$\text{Difference}=42-18=24\text{liters}$

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