Average of a team under replacements: A cricket team’s average age is 27 years. Two players aged 24 and 27 are replaced by new players aged 23 and 28. What is the new average age of the team?

Introduction / Context:
Average problems with replacements can often be handled by comparing total sums before and after. If the net change in total age is zero, the average remains unchanged (provided the team size is unchanged).

Given Data / Assumptions:

• Original team average = 27 years (team size constant).
• Removed: 24 and 27; Added: 23 and 28.

Concept / Approach:
Compute the total change: (23 + 28) − (24 + 27) = 51 − 51 = 0. Therefore, team total remains the same and so does the average.

Step-by-Step Solution:
1) Outgoing sum = 24 + 27 = 51.2) Incoming sum = 23 + 28 = 51.3) Net change = 0 ⇒ Average unchanged = 27 years.

Verification / Alternative check:
If the number of players stays the same, unchanged total implies unchanged average. This is independent of the actual team size.

Why Other Options Are Wrong:

• Any value other than 27 would require a non-zero net change in total age.

Common Pitfalls:
Students sometimes attempt to average the four numbers directly; only the net change in totals relative to team size matters.

Final Answer:
27 years