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?

Correct Answer: 84 liters

Let's solve the problem step-by-step to find the total quantity of mixture A.

Step 1: Express the quantities in Mixture A

Given that the ratio of milk and water in mixture A is 9 : 5, let:

$\text{Quantity of milk in mixture A}=9x$

$\text{Quantity of water in mixture A}=5x$

$\text{Total quantity of mixture A}=9x+5x=14x$

Step 2: Express the quantities in Mixture B

1. The quantity of milk in mixture B is 20% more than that in mixture A:

$\text{Milk in B}=9x\times (1+0.20)=9x\times 1.2=10.8x$

2. The quantity of water in mixture A is 25% more than that in mixture B:

$\text{Water in A}=\text{Water in B}\times (1+0.25)$

$5x=\text{Water in B}\times 1.25$

$\text{Water in B}=\frac{5x}{1.25}=4x$

Step 3: Use the total quantity of water to solve for x

The sum of the quantity of water in both mixtures is given as 54 liters:

$\text{Water in A}+\text{Water in B}=54$

$5x+4x=54$

$9x=54$

$x=6$

Step 4: Find the total quantity of mixture A

$\text{Total quantity of mixture A}=14x=14\times 6=84\text{liters}$

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