A storage tank contains three different chemical solvents, A, B, and C, mixed in the proportion of 4 : 6 : 5. First, 20 liters of the mixture is extracted from the tank. Subsequently, 10 liters of solvent A and 15 liters of solvent B are poured into the tank. If the final volume of solvent B exceeds the final volume of solvent A by 25 liters, calculate the original total volume of the mixture in the tank.

Correct Answer: 170L

Let's solve this problem step-by-step to find the original total volume of the mixture in the tank.

Step 1: Define initial quantities using the given ratio.

The initial ratio of solvents A, B, and C is 4 : 6 : 5.
Let the initial total volume of the mixture be $V$ liters.
The total ratio parts = $4+6+5=15$ parts.

Therefore, the initial quantities of solvents A, B, and C in terms of total volume $V$ are:

Initial volume of A = $\frac{4}{15}V$

Initial volume of B = $\frac{6}{15}V$

Initial volume of C = $\frac{5}{15}V$

Step 2: Calculate the amount of each solvent extracted.

When 20 liters of the mixture is extracted, the solvents are removed in the same ratio of 4 : 6 : 5.

Volume of solvent A extracted = $\frac{4}{15}\times 20=\frac{16}{3}$ liters

Volume of solvent B extracted = $\frac{6}{15}\times 20=8$ liters

Step 3: Determine the remaining amounts of A and B before adding fresh solvents.

Remaining volume of A = $\frac{4}{15}V-\frac{16}{3}$ liters

Remaining volume of B = $\frac{6}{15}V-8$ liters

Step 4: Calculate final volumes of A and B after additions.

Subsequently, 10 liters of solvent A and 15 liters of solvent B are added to the tank.

Final volume of A = $\left(\frac{4}{15}V-\frac{16}{3}\right)+10=\frac{4}{15}V+\frac{14}{3}$ liters

Final volume of B = $\left(\frac{6}{15}V-8\right)+15=\frac{6}{15}V+7$ liters

Step 5: Set up the equation using the final difference.

We are given that the final volume of solvent B exceeds the final volume of solvent A by 25 liters:

$\text{Final volume of B}-\text{Final volume of A}=25$

$\left(\frac{6}{15}V+7\right)-\left(\frac{4}{15}V+\frac{14}{3}\right)=25$

Simplifying the equation:

$\frac{2}{15}V+7-\frac{14}{3}=25$

$\frac{2}{15}V+\frac{7}{3}=25$

$\frac{2}{15}V=25-\frac{7}{3}$

$\frac{2}{15}V=\frac{68}{3}$

Multiply both sides by 15:

$2V=68\times 5$

$2V=340$

$V=170$

Therefore, the original total volume of the mixture in the tank was 170L.