How the Average Age of a Cricket Team Increases with Player Replacement

Understanding how the average age of a cricket team changes with the replacement of players can provide valuable insights into team dynamics and player performance. This article will walk you through a practical problem-solving scenario that illustrates the process.

Problem Statement

Given a cricket team of 11 players, two players aged 18 and 20 years are replaced with two new players. As a result, the average age of the team increases by 2 months. The question is: what is the average age of the new players?

Steps to Solve the Problem

1.

Convert the Age Increase from Months to Years

First, let's convert the age increase from months to years.

2 months (frac{2}{12}) years (frac{1}{6}) years

2.

Calculate the Total Age Increase for the Team

The increase in the average age for the team of 11 players is calculated as follows:

Total age increase 11 × (frac{1}{6}) (frac{11}{6}) years

3.

Calculate the Total Age of the Original Players

Let S be the total age of the original 11 players. The total age after replacing the two players becomes:

S - 18 - 20 x1 x2 S (frac{11}{6})

Rearranging the equation:

x1 x2 S (frac{11}{6}) - S 4.

Calculate the Total Age of the New Players

Rearranging the equation further:

x1 x2 38 (frac{11}{6}) (frac{228}{6}) (frac{11}{6}) (frac{239}{6}) 5.

Congruently, Calculate the Average Age of the New Players

To find the average age of the new players:

Average age of new players (frac{x1 x2}{2} frac{frac{239}{6}}{2} frac{239}{12})

Converting to decimal:

(frac{239}{12}) ≈ 19.9167 years ≈ 19 years and 11 months

Equivalent Solution

Another approach to solve the problem also yields the same result:

1.

Convert the Age Increase from Months to Years

2 months 1.83 years

2.

Calculate the Total Age Increase for the Team

Total age increase 11 × 1.83 19.83 years

3.

Calculate the Total Age of the Original Players

Total age of original players 38 years

4.

Calculate the Total Age of the New Players

Total age of new players 39.83 years

5.

Congruently, Calculate the Average Age of the New Players

Average age of new players 39.83 / 2 ≈ 19.915 years

6.

Further Simplified Solution

Using a different approach:

1.

Convert the Age Increase from Months to Years

2 months (frac{1}{6}) years

2.

Convert the Total Age Increase to the Same Denominator

11y - 19 z10 z11 11y - 11/6

Rearranging the equation:

z10 z11 103/6

3.

Calculate the Average Age of the New Players

Average age of new players (103/6) / 2 103/12 ≈ 8.58 years

Conclusion

The average age of the new players, in both scenarios, is approximately 19 years and 11 months. This problem-solving approach demonstrates a step-by-step method to calculate the average age of players in a cricket team after a change in the team composition. Understanding these calculations can aid in making informed decisions about team selection and strategic planning.