Vessel P contains 200 liters of a mixture of milk and water in which water is 35%. y liters of the mixture are taken out, where the quantity of water in y liters is 21 liters. This y liters are then poured into vessel Q, which already contains y liters of water. Find the difference between the quantity of milk and water in the resultant mixture of vessel Q (in liters).

The correct answer is 42.

Step-by-Step Explanation:

Step 1: Analyze the initial mixture in Vessel P
Vessel P contains a total of 200 liters of a mixture of milk and water.
Percentage of water in Vessel P = 35%
Percentage of milk in Vessel P = 100% - 35% = 65%

Step 2: Find the value of y
When y liters of the mixture are taken out from Vessel P, the ratio of milk and water in the removed mixture remains the same as in Vessel P.
Therefore, the concentration of water in the y liters of mixture is also 35%.
Given that the quantity of water in y liters is 21 liters, we can write:
35% of y = 21 liters

$\frac{35}{100}\times y=21$

$y=\frac{21\times 100}{35}$

$y=60\text{liters}$

So, the total volume of mixture taken out is 60 liters. Within this y (60) liters of mixture:
Quantity of water = 21 liters
Quantity of milk = 60 - 21 = 39 liters

Step 3: Analyze Vessel Q
Vessel Q already contains y liters of water. Since y = 60, Vessel Q contains 60 liters of water.
Now, the y liters of mixture taken from Vessel P is poured into Vessel Q.
In the resultant mixture of Vessel Q:
Total quantity of water = (Initial water in Q) + (Water added from mixture) = 60 + 21 = 81 liters
Total quantity of milk = Milk added from mixture = 39 liters

Step 4: Find the difference between the quantities of milk and water in Vessel Q
Difference = Quantity of water - Quantity of milk
Difference = 81 - 39 = 42 liters