Let’s denote the average age of the original eight guys as $A$. So, the total age of the original group is $8A$.

When two men aged 21 and 23 are replaced, the group's average age rises by 2 years. Thus, the new average becomes $A + 2$, and the total age of the group becomes $8(A + 2) = 8A + 16$.

The two new men added are aged $x$ and $y$. So, the equation is:

$8A - (21 + 23) + (x + y) = 8A + 16$

Simplifying this:

$x + y - 44 = 16$ $x + y = 60$

Therefore, the average age of the two new men is:

$\frac{x + y}{2} = \frac{60}{2} = 30$

The average age of the two new men is 30 years.

Would you like further explanation or have questions? Here are some related problems:

1. How does replacing members in a group affect the average in general?
2. What would happen if the average age had increased by three years instead?
3. Can you find the ages of the two new men if given another condition?
4. How does the average change if two younger people join the group?
5. What if the two men replaced had been the oldest in the group?

Tip: When replacing elements in an average, calculate the net effect on the total first, then apply it to the average change.