The given problem can be solved using the concept of average age and the addition and subtraction of ages.

Given:
- There are 8 persons in a committee.
- When two men are replaced by two women, the average age of the committee increases by 2 years.
- The ages of the replaced men are 35 years and 45 years.

Approach:
To solve this problem, we can follow these steps:
1. Find the total age of the committee before the replacement.
2. Find the total age of the committee after the replacement.
3. Find the difference in the total ages before and after the replacement.
4. Divide the difference in total ages by the number of persons to find the increase in average age.
5. Subtract the increase in average age from the average age before the replacement to get the average age of the two women.

Calculations:
Let's calculate step by step:

1. Find the total age of the committee before the replacement:
- Let the sum of ages of the 8 persons before the replacement be X.

2. Find the total age of the committee after the replacement:
- After replacing the two men, the total age of the committee will be X - 35 - 45 + 2y, where y is the average age of the two women.

3. Find the difference in the total ages before and after the replacement:
- Difference = (X - 35 - 45 + 2y) - X = -80 + 2y

4. Divide the difference in total ages by the number of persons to find the increase in average age:
- Increase in average age = (-80 + 2y) / 8 = -10 + 0.25y

5. Subtract the increase in average age from the average age before the replacement to get the average age of the two women:
- Average age before replacement = X / 8
- Average age after replacement = Average age before replacement + 2 (as given)
- Average age after replacement = X / 8 + 2

Using the given information, we can equate the average age after replacement with the average age of the two women:
X / 8 + 2 = y

Simplifying the equation, we get:
X + 16 = 8y
y = (X + 16) / 8

Substituting the value of y in the equation for increase in average age:
Increase in average age = -10 + 0.25[(X + 16) / 8]

Since the increase in average age is given as 2 years, we can solve the equation for X:
-10 + 0.25[(X + 16) / 8] = 2

Solving the equation, we get:
X + 16 = 80
X = 64

Substituting the value of X in the equation for y, we get:
y = (64 + 16) / 8 = 80 / 8 = 10

Therefore, the average age of the two women is 10 years.