The ratio of milk and water in mixture A is 9: 5. The quantity of milk in mixture B is 20% more that in mixture A and quantity of water in mixture A is 25% more than that in mixture B. If sum of quantity of water of both mixture is 54 liters, then find the total quantity of mixture in A.

The correct answer is 84 liters.

Let us solve the problem step-by-step by defining variables for the quantities of milk and water in mixture A and mixture B.

Step 1: Express the quantities of milk and water in mixture A.
Given that the ratio of milk and water in mixture A is 9 : 5.
Let the quantity of milk in mixture A = $9x$ liters.
Let the quantity of water in mixture A = $5x$ liters.

Step 2: Express the quantities of milk and water in mixture B.
1. The quantity of milk in mixture B is 20% more than that in mixture A:
$\text{Milk in B}=9x+0.20\times 9x=1.20\times 9x=10.8x$ liters.

2. The quantity of water in mixture A is 25% more than that in mixture B:
This means:
$\text{Water in A}=1.25\times \left(\text{Water in B}\right)$

$5x=\frac{5}{4}\times \left(\text{Water in B}\right)$

$\text{Water in B}=5x\times \frac{4}{5}=4x$ liters.

Step 3: Use the given sum of the quantity of water in both mixtures to find $x$.
The sum of the quantity of water in both mixture A and mixture B is 54 liters:
$\text{Water in A}+\text{Water in B}=54$

$5x+4x=54$

$9x=54$

$x=\frac{54}{9}=6$

Step 4: Calculate the total quantity of mixture in A.
The total quantity of mixture A is the sum of milk and water in mixture A:
$\text{Total quantity of mixture A}=9x+5x=14x$

Substituting $x=6$ into the equation:
$\text{Total quantity of mixture A}=14\times 6=84$ liters.

Thus, the total quantity of mixture in A is 84 liters.