In a project team, the average age of 6 members is 22 years. When the manager's age is excluded, the average age of the remaining team members drops by 2 years. What is the manager's age?

The correct answer is 32.

Step 1: Calculate the total age of all 6 project team members.
We are given that the average age of the 6 members (which includes the manager) is 22 years.
Using the formula for average:

$\text{Average}=\frac{\text{Total Sum}}{\text{Number of Items}}$

We can find the total age of all 6 members by multiplying the average age by the total number of members:

$\text{Total age of 6 members}=22\times 6=132\text{years}$

Step 2: Calculate the total age of the remaining 5 team members.
When the manager's age is excluded, the number of remaining members becomes 6 - 1 = 5.
The average age drops by 2 years, which means the new average age is:

$\text{New average age}=22-2=20\text{years}$

Now, calculate the total age of these remaining 5 team members:

$\text{Total age of 5 members}=20\times 5=100\text{years}$

Step 3: Determine the manager's age.
The manager's age is simply the difference between the total age of the original 6 members and the total age of the remaining 5 members:

$\text{Manager's age}=\text{Total age of 6 members}-\text{Total age of 5 members}$

$\text{Manager's age}=132-100=32\text{years}$

Therefore, the manager's age is 32 years.