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 :

Answer: Option C

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,
$$\begin{array}{rl}& \Rightarrow 11x+y-18-20=11\left(x+\frac{1}{6}\right)\\ & \Rightarrow 11x+y-38=11x+\frac{11}{6}\\ & \Rightarrow y=\frac{11}{6}+38\\ & \Rightarrow y=\frac{239}{6}\end{array}$$
∴ Average
$$\begin{array}{rl}& =\frac{239}{2\times 6}\\ & =\frac{239}{12}\end{array}$$
= 19 years 11 months