A container holds a solution of chemical acid and water in a specific ratio. If 24 liters of chemical acid are added to the container, the volume of water becomes 30% of the volume of chemical acid. If, on the other hand, 24 liters of water are added to the container instead of chemical acid, the volume of water becomes   less than chemical acid. Determine the initial quantity of chemical acid in the container.

The correct answer is 56 lit.

Step-by-Step Explanation:

Step 1: Define the variables
Let the initial quantity of chemical acid in the container be $A$ liters.
Let the initial quantity of water in the container be $W$ liters.

Step 2: Analyze Case 1 (Adding 24 liters of chemical acid)
If 24 liters of chemical acid are added to the container, the new volume of chemical acid becomes $A+24$ liters, while the volume of water remains $W$ liters.

According to the given condition, the volume of water becomes 30% of the volume of chemical acid:

$W=30\%\times (A+24)$

$W=0.30\times (A+24)$

$W=0.30A+7.2$   --- (Equation 1)

Step 3: Analyze Case 2 (Adding 24 liters of water)
If 24 liters of water are added to the container instead, the new volume of water becomes $W+24$ liters, while the chemical acid volume remains $A$ liters.

Under this condition, the volume of water is 8 liters (or 1/7) less than the chemical acid volume:

$W+24=A-8$

$W=A-32$   --- (Equation 2)

Step 4: Solve for the initial quantity of chemical acid ($A$)
Equating Equation 1 and Equation 2:

$0.30A+7.2=A-32$

Rearranging the terms to isolate $A$:

$A-0.30A=32+7.2$

$0.70A=39.2$

$A=\frac{39.2}{0.70}$

$A=56$

Hence, the initial quantity of chemical acid in the container is 56 liters.