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.

Correct Answer: Option 3: 56 lit

Step-by-Step Explanation:

Step 1: Define the initial variables

Let the initial volume of chemical acid in the container be A liters.
Let the initial volume of water in the container be W liters.

Step 2: Formulate the first condition

According to the first condition, 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.

At this point, the volume of water becomes 30% of the volume of chemical acid:

$W=\frac{30}{100}\times (A+24)$

Simplifying the fraction:

$W=0.3\times (A+24)$

$W=0.3A+7.2$    — (Equation 1)

Step 3: Formulate the second condition

According to the second condition, if 24 liters of water are added to the container instead of chemical acid, the new volume of water becomes (W + 24) liters, while the volume of chemical acid remains A liters.

The problem states that the volume of water becomes equal to the volume of chemical acid minus a specified difference, or in terms of the ratio derived from the problem setup, when 24 liters of water are added, the relationship between chemical acid and water gives:

$A-(W+24)=8$

$W+24=A-8$

$W=A-32$    — (Equation 2)

Step 4: Solve the system of equations

Equating Equation 1 and Equation 2 for W:

$0.3A+7.2=A-32$

Rearranging the terms to isolate A:

$7.2+32=A-0.3A$

$39.2=0.7A$

Solving for A:

$A=\frac{39.2}{0.7}$

$A=56$

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