In a low-scoring T20 match, the chasing team won by 10 wickets — both openers…

Concept: The average of a group equals the total sum of its values divided by the number of values. When a group splits into two subgroups, the whole group's total sum equals the sum of the first subgroup's total plus the second subgroup's total (count times its average).

Application:

1. A 10-wicket win means both openers remained unbeaten and completed the chase without any wicket falling, so the remaining 9 players never got a turn to bat.

2. The first opener's age is 31 years. The second opener, being 11 years younger, is 31 minus 11 equals 20 years. Together, the two openers' combined age is 51 years.

3. Let the team's overall average age be x years. The total age of all 11 players is then 11x.

4. The 9 players who did not bat have an average age of (x + 1) years, since it is stated to be one year more than the team average. Their total age is therefore 9(x + 1).

5. The total age of the whole team equals the batters' total age plus the non-batters' total age: 11x = 51 + 9(x + 1).

6. Expanding and solving: 11x = 51 + 9x + 9, so 11x minus 9x = 60, giving 2x = 60, so x = 30.

Cross-check: Checking back: with x = 30, the non-batters' average is 31, so their total age is 9 times 31 equals 279; the batters' total is 51; the grand total is 330, which equals 11 times 30. This matches, confirming the value.

Answer: Therefore, the average age of the team is 30 years.