The average age of the 11 players of a cricket team increases by 2 months when two of them, aged 18 years and 20 years, are replaced by two new players. What is the average age of the two new players?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 19 years 11 months
When members are replaced, the total age rises by the rise in the average times the number of players. The two new players together must be that much older than the two who left.
Rise in the total age \(=11\times2=22\) months \(=1\) year 10 months
Total age of the two players who left \(=18+20=38\) years
Total age of the two new players \(=38\) years \(+\,1\) year 10 months \(=39\) years 10 months
39 years 10 months \(=39\times12+10=478\) months
Average age of the new players \(\displaystyle =\frac{478}{2}=239\) months \(=19\) years 11 months
The average age of the new players is 19 years 11 months.