In a cricket team, the average age of 11 players decreases by 2 months when two players aged 17 years and 20 years are replaced by two reserves. What is the average age of the two reserves?

Introduction:
This average-age replacement problem asks you to translate a change in average (2 months) into a change in total age for the whole team, and then use that to determine the combined and average ages of the two incoming reserve players.

Given Data / Assumptions:

• Team size = 11 players.
• Two outgoing ages: 17 years and 20 years.
• Average decreases by 2 months = 2/12 years = 1/6 year.
• Two incoming reserves replace the outgoing players.

Concept / Approach:
A change in average by Δ across n people changes the total by n * Δ. Here Δ = −1/6 year. So total decreases by 11 * (1/6) = 11/6 years. That total decrease must equal (sum of reserves) − (sum of outgoing). Solve for the reserves’ total, then divide by 2 to get their average.

Step-by-Step Solution:

Verification / Alternative check:
If each player’s average drops by 2 months, the group total must drop by 11 * 2 months = 22 months = 1 year 10 months, exactly the difference between outgoing and incoming totals computed above.

Why Other Options Are Wrong:
17 years 1 month, 17 years 11 months, 18 years 3 months, and 16 years 9 months do not produce the exact 22-month reduction in total age when compared to the outgoing pair (17 and 20).

Common Pitfalls:
Forgetting to multiply the average change by the team size, or averaging the two outgoing ages directly with the 2-month change instead of working with totals.

Final Answer:
17 years 7 months