A container contains mixture of milk and water in which milk is 50% more than that of water. If four liter of milk added in the vessel, then milk becomes 100% more than water in the resultant mixture. Find the initial quantity of mixture?

The correct option is 20 liter.

Let us find the initial quantity of the mixture step-by-step.

Step 1: Understand the initial ratio of milk and water
Let the initial quantity of water in the container be $x$ liters.
According to the problem, the quantity of milk is $50\%$ more than that of water.
Therefore, the initial quantity of milk is:
$\text{Milk}=x+50\%\text{of}x=x+0.5x=1.5x$
Thus, the initial quantity of the mixture is:
$\text{Initial Mixture}=\text{Milk}+\text{Water}=1.5x+x=2.5x$

Step 2: Formulate the equation after adding milk
When $4$ liters of milk are added to the vessel:
New quantity of milk = $1.5x+4$ liters.
The quantity of water remains unchanged at $x$ liters.
In the new mixture, milk is $100\%$ more than water. This means the quantity of milk is twice the quantity of water:
$\text{New Milk}=x+100\%\text{of}x=2x$

Step 3: Solve for $x$
Equating the new quantity of milk expressions:
$1.5x+4=2x$
Subtract $1.5x$ from both sides:
$4=2x-1.5x$
$0.5x=4$
$x=\frac{4}{0.5}=8$
So, the initial quantity of water is $8$ liters.

Step 4: Calculate the initial quantity of the mixture
Substitute the value of $x$ back into the initial mixture expression:
$\text{Initial Mixture}=2.5x=2.5\times 8=20\text{liters}$

Hence, the initial quantity of the mixture is 20 liter.