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's break down the problem step-by-step to find the initial quantity of the mixture.

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

Step 2: Set up the equation for the new mixture
When 4 liters of milk is added to the container, the new quantity of milk becomes:
$\text{New Milk}=1.5x+4$
The quantity of water remains unchanged at $x$ liters.
According to the problem, the new quantity of milk is 100% more than water in the resultant mixture:
$\text{New Milk}=\text{Water}+100\%\text{of}\text{Water}=x+x=2x$

Step 3: Solve for x
We can now equate the two expressions for the new quantity of milk:
$1.5x+4=2x$
Subtract $1.5x$ from both sides of the equation:
$4=2x-1.5x$
$0.5x=4$
Multiply both sides by 2:
$x=8$
So, the initial quantity of water was 8 liters.

Step 4: Find the initial quantity of the mixture
Substitute the value of $x$ back into our expression for the initial mixture:
$\text{Initial Mixture}=2.5x=2.5\times 8=20\text{liters}$
Thus, the initial quantity of the mixture was 20 liters.