The average age of a team of 12 players is 23 years. If the age of the coach is also included, the average age increases by 2 years. What is the age of the coach in years?

Introduction / Context:
This is a standard average age problem used in aptitude exams. A sports team has a known average age for its players. When the coach is added to the group, the average age increases by a fixed amount. From this new information you are asked to calculate the coach age. The question checks your comfort with converting averages to totals and then working backward to find an unknown value.

Given Data / Assumptions:
- Number of players in the team = 12.
- Average age of the 12 players = 23 years.
- When the coach is included, total members = 13.
- New average age including the coach = 23 + 2 = 25 years.
- We must find the age of the coach in years.

Concept / Approach:
The fundamental concept is that average age multiplied by the number of persons gives the total of all ages. First compute the total age of the 12 players. Then compute the total age of the 12 players plus the coach using the new average. The difference between these two totals must be the coach age. This simple method avoids unnecessary algebra and works very well in age based questions.

Step-by-Step Solution:
Step 1: Total age of the 12 players = average * number of players = 23 * 12.Step 2: Compute this value: 23 * 12 = 276 years.Step 3: After including the coach, there are 13 persons and the average age is 25 years.Step 4: Total age of players plus coach = 25 * 13.Step 5: Compute this value: 25 * 13 = 325 years.Step 6: Coach age = combined total age minus total age of players = 325 - 276.Step 7: Therefore, coach age = 49 years.

Verification / Alternative check:
To verify, consider the group with the coach. If the coach is 49 and the players together are 276 years, then the total age is 276 + 49 = 325 years. Dividing by 13 gives an average of 325 / 13 = 25 years, which matches the stated new average. The original average of 23 years for 12 players is already satisfied by the total 276, so all the given conditions are consistent with a coach age of 49 years.

Why Other Options Are Wrong:
If the coach were 41, 47 or 51 years old, then the total age for 13 persons would be different and the resulting average would not be exactly 25 years. You can quickly check by adding each option to 276 and dividing by 13. None of those values except 49 yields an average of 25, so they cannot be correct.

Common Pitfalls:
Some learners mistakenly increase the total age by 2 years instead of understanding that the average increased by 2 across all 13 members. Others forget to update the number of persons from 12 to 13 when computing the new total. Always remember that an increase in average across a larger group corresponds to a much larger increase in total, which must be handled by multiplication.

Final Answer:
The age of the coach is 49 years.