The average age of the district level hockey team of eleven players is 22 years. When the age of the coach is also included, the average age increases by 1 year. What is the age of the coach?

Introduction / Context:
This problem uses the idea of average age before and after adding one more person. It shows how including an older person raises the group average and how you can work backward to find that person's age.

Given Data / Assumptions:
- There are 11 players with an average age of 22 years.
- When the coach is added, there are 12 people and the new average age is 23 years (one year higher).
- We need to find the age of the coach.

Concept / Approach:
Average age is total age divided by the number of people. We find the total age of the players alone from the first average. Then we find the total age of players plus coach from the second average. The difference between these two totals is the coach's age.

Step-by-Step Solution:
Step 1: Total age of the 11 players = 22 * 11. Step 2: Compute 22 * 11 = 242 years. Step 3: When the coach is added, there are 12 people with average 23 years, so the new total age is 23 * 12. Step 4: Compute 23 * 12 = 276 years. Step 5: The age of the coach = total with coach - total without coach = 276 - 242. Step 6: Calculate 276 - 242 = 34 years.

Verification / Alternative check:
Check by recomputing the final average. If you have 11 players totaling 242 years and a coach of 34 years, the total is 276. Dividing by 12 gives 23 years as required, so the age 34 is consistent.

Why Other Options Are Wrong:
- Option 33 yrs: This would give a total of 275 and an average slightly less than 23.

- Option 35 yrs: This would give a total of 277 and an average greater than 23.

- Option 36 yrs: This would yield an even higher total and average, inconsistent with the given new average of 23.

Common Pitfalls:
Some learners mistakenly average the two averages (22 and 23) instead of working with totals. Others forget to multiply the average by the number of people to get the sum. Always remember that changes in average correspond to changes in total sum, which you can track directly.

Final Answer:
The coach is 34 yrs old.