A batch of seven storage tanks has an average volume of 40 liters. One tank in the batch is swapped with a new tank holding 60 liters, which causes the average volume of the batch to rise by two liters. Determine the volume of the tank that was replaced.

The correct option is 46 liters.

Step 1: Determine the initial total volume of the tanks
We are given that the batch consists of 7 storage tanks with an average volume of 40 liters.
The total volume of all 7 tanks combined initially can be calculated by multiplying the number of tanks by the initial average volume:

$\text{Initial Total Volume}=7\times 40=280\text{liters}$

Step 2: Determine the new total volume after replacement
Replacing one tank causes the average volume of the 7 tanks to increase by 2 liters.
Therefore, the new average volume per tank is:

$\text{New Average Volume}=40+2=42\text{liters}$

Now, calculate the new total volume for the 7 tanks using this updated average:

$\text{New Total Volume}=7\times 42=294\text{liters}$

Step 3: Calculate the overall increase in batch volume
The overall increase in volume across all 7 tanks is the difference between the new total volume and the initial total volume:

$\text{Increase in Total Volume}=294-280=14\text{liters}$

Step 4: Find the volume of the tank that was replaced
The 14-liter net increase occurred because an old tank of volume $x$ was replaced by a new tank holding 60 liters.
The difference between the new tank's volume and the old tank's volume must equal this total volume increase:

$60-x=14$

Solving for $x$:

$x=60-14=46\text{liters}$

Thus, the volume of the storage tank that was replaced is 46 liters.