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.

Correct Answer: The correct option is 46 liters.

Step-by-step Explanation:

Step 1: Calculate the initial total volume of the batch.
We are given that a batch of 7 storage tanks has an initial average volume of 40 liters.
The total volume of a set of items is equal to the number of items multiplied by their average value.

$\text{Initial Total Volume}=\text{Number of Tanks}\×\text{Initial Average Volume}$

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

Step 2: Calculate the new average volume and total volume after the replacement.
Replacing one tank causes the average volume of the batch to rise by 2 liters.

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

Since the number of tanks remains 7, the new total volume of the batch is:

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

Step 3: Determine the volume of the replaced tank.
Let $V$ be the volume of the tank that was replaced.
When a tank of volume $V$ is removed and replaced by a new tank of 60 liters, the new total volume can be expressed as:

$\text{New Total Volume}=\text{Initial Total Volume}-V+60$

Substitute the calculated values into the equation:

$294=280-V+60$

$294=340-V$

$V=340-294$

$V=46\text{\ liters}$

Conclusion:
The volume of the tank that was replaced is 46 liters.