Given:
- The average age of 11 players of a cricket team is increased by 2 months when two players aged 18 years and 20 years are replaced by two new players.
- We need to find the average age of the new players.

Approach:
To solve this problem, we can use the concept of averages. We'll calculate the sum of ages before and after the replacement, and then find the difference in the average ages.

Let's solve this step by step:

Step 1: Calculate the sum of ages before replacement:
- We know that the average age of the 11 players is increased by 2 months when two players aged 18 years and 20 years are replaced.
- So, the sum of ages before replacement = average age before replacement * number of players
- Let's assume the average age before replacement is A (in years) and the number of players is 11.
- Therefore, the sum of ages before replacement = A * 11

Step 2: Calculate the sum of ages after replacement:
- After replacing the 18-year-old and 20-year-old players, the average age increases by 2 months.
- Let's assume the average age after replacement is B (in years).
- Therefore, the sum of ages after replacement = B * 11

Step 3: Find the difference in the average ages:
- The difference in the average ages = average age after replacement - average age before replacement
- We know that the average age after replacement is increased by 2 months compared to the average age before replacement.
- So, the difference in the average ages = 2 months

Step 4: Calculate the sum of ages of the new players:
- We replaced two players with ages 18 years and 20 years.
- So, the sum of ages of the new players = (sum of ages after replacement) - (sum of ages before replacement)
- Therefore, the sum of ages of the new players = (B * 11) - (A * 11)

Step 5: Calculate the average age of the new players:
- Since the sum of ages of the new players is known, we can divide it by the number of new players to get the average age of the new players.
- Let's assume the number of new players is 2.
- Therefore, the average age of the new players = (sum of ages of the new players) / (number of new players)
- Therefore, the average age of the new players = [(B * 11) - (A * 11)] / 2

Step 6: Simplify the expression:
- Average Age of New Players = [(B * 11) - (A * 11)] / 2
- Simplifying this expression gives, Average Age of New Players = (B - A) * 11 / 2

Step 7: Substitute the given information:
- We know that the difference in average ages is 2 months, which is equivalent to 2/12 = 1/6 years.
- So, (B - A) = 1/6
- Substituting this into the expression for the average age of new players:
Average Age of New Players = (1/