Calculating the Average Age of New Players in Cricket

Understanding the Problem

When a cricket team's average age decreases by 2 months, it means two new players are replacing two older ones. This scenario requires us to calculate the average age of the new players based on given data.

Solving the Problem

Let's denote the age of the 11 players (formally x1, x2, ..., x11) as emY/em separately and initially having an average age of emY/em.

Given players' ages in the team were:
x1, x2, ..., x9 (known ages) 17 years and 2 years respectively
Let the new players' ages be z10 and z11.

The steps to solve the problem are as follows:

Step 1: Calculate the Initial Total Age and Average

Let the average age of the initial team be emY/em.

Thus, the total age of the team is 11Y.

Given the ages of the specific players:

x10 17 years
x11 2 years.

From this, the total age of the first 9 players, excluding the last two, is: 11Y - (17 2) 11Y - 19.

Let's denote the average of the initial 9 players as emy/em.

Step 2: Incorporate the New Players

When the two new players replace the two older ones, the average age of the team increases by 2 months, which is 1/6 of a year.

The new total age of the team is 11Y (z10 z11) - (17 2)

The new average age is now emY/em 1/6.

Thus, we can write the new average equation as:

(em11Y - 19 z10 z11/em) / 11 emY/em 1/6

Substituting em11Y - 19/em from the initial total age:

(11Y - 19 z10 z11) / 11 emY/em 1/6

Multiplying through by 11:

11Y - 19 z10 z11 11Y 11/6

Subtracting 11Y from both sides:

-19 z10 z11 11/6

Simplifying:

z10 z11 11/6 19 11/6 114/6 125/6.

This implies the combined age of the new players:

z10 z11 20.8333 years,

Or 20 years and 10 months.

Step 3: Calculate the Average Age of the New Players

To find the average age of the two new players, we divide the total age of the new players by 2:

Average age of new players (z10 z11) / 2 20.8333 / 2 10.4167 years.

This can be rounded to 10 years and 5 months, or 10.42 years.

Conclusion

The average age of the new players is approximately 10.42 years. This calculation is crucial for coaches and team managers to understand the impact of player changes on the team's average age and overall squad composition.

Understanding these calculations can help in strategic planning, team balancing, and overall performance analysis in cricket teams.