Two identical storage tanks are filled to 35% and 60% of their total capacities with liquid A, respectively. Both tanks are then topped off completely with liquid B. If the contents of both tanks are emptied and thoroughly blended in a larger reservoir, what percentage of the combined mixture will consist of liquid B?

The correct answer is 52.5%.

Step-by-Step Explanation:

Step 1: Define the capacity of the tanks
Let the total capacity of each identical storage tank be represented by $V$.

Since both tanks are identical and filled completely, the total volume of the combined mixture in the larger reservoir is:

$\text{Total Combined Volume}=V+V=2V$

Step 2: Calculate the amount of Liquid B in Tank 1
Tank 1 is filled to 35% of its total capacity with liquid A.
Since the remaining capacity of Tank 1 is topped off completely with liquid B, the percentage of liquid B in Tank 1 is:

$100\%-35\%=65\%$

In terms of volume, the amount of liquid B in Tank 1 is:

$\text{Liquid B in Tank 1}=0.65\times V=0.65V$

Step 3: Calculate the amount of Liquid B in Tank 2
Tank 2 is filled to 60% of its total capacity with liquid A.
Since the remaining capacity of Tank 2 is topped off completely with liquid B, the percentage of liquid B in Tank 2 is:

$100\%-60\%=40\%$

In terms of volume, the amount of liquid B in Tank 2 is:

$\text{Liquid B in Tank 2}=0.40\times V=0.40V$

Step 4: Find the total volume of Liquid B in both tanks
Adding the volume of liquid B from both storage tanks gives:

$\text{Total Liquid B}=0.65V+0.40V=1.05V$

Step 5: Calculate the overall percentage of Liquid B in the combined mixture
The percentage of liquid B in the combined mixture is the ratio of total liquid B volume to the total combined volume, multiplied by 100%:

$\text{Percentage of Liquid B}=\left(\frac{1.05V}{2V}\right)\times 100\%$

Simplifying the fraction by canceling out $V$:

$\text{Percentage of Liquid B}=0.525\times 100\%=52.5\%$

Thus, liquid B makes up 52.5% of the combined mixture.