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 :
A. 19 years 1 month B. 19 years 6 months C. 19 years 11 months D. 19 years 5 months Answer: Option CShow Answer
Solution(By Apex 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, $\begin{aligned}&\Rightarrow11x+y-18-20=11\left(x+\frac{1}{6}\right)\\ &\Rightarrow11x+y-38=11x+\frac{11}{6}\\ &\Rightarrow y=\frac{11}{6}+38\\ &\Rightarrow y=\frac{239}{6}\\ &\text{ Average }\\ &=\frac{239}{2\times6}\\ &=\frac{239}{12}\end{aligned}$ = 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, $\begin{aligned}&\Rightarrow11x+y-18-20=11\left(x+\frac{1}{6}\right)\\ &\Rightarrow11x+y-38=11x+\frac{11}{6}\\ &\Rightarrow y=\frac{11}{6}+38\\ &\Rightarrow y=\frac{239}{6}\\ &\text{ Average }\\ &=\frac{239}{2\times6}\\ &=\frac{239}{12}\end{aligned}$ = 19 years 11 months
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