Container A contains 300 liters of a mixture of orange juice and water, in which water is 40%. A volume of k liters of the mixture is extracted, where the amount of water in k liters is 32 liters. This k liters is then poured into Container B, which already holds k liters of pure water. Find the difference between the volume of juice and water in the resulting mixture in Container B (in liters).

The correct answer is 64.

Step 1: Find the extracted volume, k.
Container A contains a mixture in which water is 40%. Any portion extracted from this container will also maintain the same concentration of 40% water.
We are given that the amount of water in k liters of extracted mixture is 32 liters.

$40\%\text{of}k=32$

$\frac{40}{100}\times k=32$

$0.4\times k=32$

$k=\frac{32}{0.4}=80\text{liters}$

Step 2: Calculate the components in the extracted k liters of mixture.
Total extracted mixture volume, k = 80 liters.
Volume of water extracted = 32 liters.
Volume of orange juice extracted = Total extracted volume - Water volume

$\text{Volume of orange juice extracted}=80-32=48\text{liters}$

Step 3: Calculate the resulting amounts of water and juice in Container B.
Container B initially contains k = 80 liters of pure water.
When the extracted 80 liters of mixture (which contains 32 liters of water and 48 liters of orange juice) is added into Container B:

Total water in Container B = Initial pure water + Water from extracted mixture

$\text{Total Water in Container B}=80+32=112\text{liters}$

Total orange juice in Container B = Orange juice from extracted mixture

$\text{Total Orange Juice in Container B}=48\text{liters}$

Step 4: Find the difference between the volume of water and orange juice in Container B.

$\text{Difference}=112-48=64\text{liters}$

Thus, the difference between the volume of juice and water in the resulting mixture in Container B is 64 liters.