The average age of 11 players of a cricket team is increased by 2 months when two of them aged 18 years and 20 years are replaced by two new players. The average age of the new players is :

Solution(By Examveda Team)

Total age of 2 players = 18 + 20 = 38 years
Increased years = 2 × 11 = 22 months
Age of new players
= 38 years + 22 months
= 39 years 10 months
Average = 19 years 11 months

Alternate
Let the total age of 11 players = 11x
Then the sum of age of new players = y years
According to the question,
$$\eqalign{ & \Rightarrow 11x + y - 18 - 20 = 11\left( {x + \frac{1}{6}} \right) \cr & \Rightarrow 11x + y - 38 = 11x + \frac{{11}}{6} \cr & \Rightarrow y = \frac{{11}}{6} + 38 \cr & \Rightarrow y = \frac{{239}}{6} \cr} $$
∴ Average
$$\eqalign{ & = \frac{{239}}{{2 \times 6}} \cr & = \frac{{239}}{{12}} \cr} $$
= 19 years 11 months