Question

The average age of 11 players of a cricket team is decreased by 2 months when two of them aged 17 years and 20 years are replaced by two new players. The average age of the new players is 

(a) 17 years 1 month 

(b) 17 years 7 months 

(c) 17 years 11 months 

(d) 18 years 3 months

Answer 1

Answer is: (b) 17 years 7 months

Let the average age of 11 players be x.

Then, total age of 11 players = 11x 

Total age of 9 players = 11x – (17 + 20) = 11x – 37 

Let y be the total age of the 2 new players. 

Then \(\frac{11x-37+y}{11}=x - \frac{1}{6} = \frac{6x-1}{6}\)

⇒ 66x – 222 + 6y = 66x – 11

⇒ 6y = –11 + 222 = 211 ⇒ y = \(\frac{211}{6}\) years 

∴ Average age of the two players = \(\frac{y}{2}\) = \(\frac{211}{12}\) = 17 years 7 months