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.

The correct option is 24.

Step 1: Determine the initial composition of Vessel A

Vessel A contains 150 liters of a mixture of milk and water, where water accounts for 40% of the total mixture.

Percentage of water in Vessel A = 40%

Percentage of milk in Vessel A = 100% - 40% = 60%

Ratio of Milk to Water in Vessel A = 60 : 40 = 3 : 2

Step 2: Find the value of 'x'

'x' liters of the mixture is taken out from Vessel A.

In any taken out portion of a mixture, the components remain in the same ratio as the original mixture.

So, in 'x' liters of the mixture, the ratio of milk to water is also 3 : 2.

We are given that the quantity of water in 'x' liters is 12 liters.

Since water represents 2 parts out of total 5 parts (3 + 2 = 5 parts):

$\frac{2}{5}\times x=12$

$x=\frac{12\times 5}{2}=30\text{liters}$

Therefore, the total quantity of mixture taken out, x = 30 liters.

Step 3: Calculate the quantity of milk in 'x' liters

Since the total quantity removed is 30 liters and water in it is 12 liters:

Quantity of milk in 'x' liters = Total removed mixture - Quantity of water removed

Quantity of milk in 'x' liters = 30 - 12 = 18 liters.

Step 4: Determine the contents of Vessel B after adding the mixture

Vessel B initially contained 'x' liters of pure water, which is 30 liters of water.

Now, 'x' liters of mixture (containing 18 liters of milk and 12 liters of water) is poured into Vessel B.

Total milk in Vessel B = 18 liters

Total water in Vessel B = Initial water + Water from 'x' liters mixture

Total water in Vessel B = 30 + 12 = 42 liters

Step 5: Find the difference between quantity of milk and water in Vessel B

Difference = Quantity of water in Vessel B - Quantity of milk in Vessel B

Difference = 42 - 18 = 24 liters.

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