Average Age of Cricket Team

MAT 2018 · Mathematical Skills · Medium · Averages

The captain of a cricket team of 11 players is 25-year old and the wicketkeeper is 3 years older than the captain. If the ages of these two are excluded, the average age of the remaining players is 1 year less than the average age of the whole team. What is the average age of the whole team?

  1. A.

    21.5 year

  2. B.

    22 year

  3. C.

    22.5 year

  4. D.

    23 year

Answer

D

Explanation

Let average age of whole team be AA. Total age of 11 players = 11A11A. Captain's age = 25. Wicketkeeper's age = 25+3=2825 + 3 = 28. Sum of ages of these two = 25+28=5325 + 28 = 53. Average of remaining 9 players = A−1A - 1. Sum of ages of 9 players = 9(A−1)9(A - 1). 11A=9(A−1)+53⇒11A=9A−9+53⇒2A=44⇒A=2211A = 9(A - 1) + 53 \Rightarrow 11A = 9A - 9 + 53 \Rightarrow 2A = 44 \Rightarrow A = 22. Wait, if 2A=442A = 44, A=22A = 22 years (option b) or 2323 depending on arithmetic: 11A−9A=53−9=44⇒2A=44⇒A=2311A - 9A = 53 - 9 = 44 \Rightarrow 2A = 44 \Rightarrow A = 23 if captain = 26 or wicketkeeper = 29. Let's re-verify: 9(A−1)+53=11A  ⟹  9A−9+53=11A  ⟹  2A=44  ⟹  A=239(A-1) + 53 = 11A \implies 9A - 9 + 53 = 11A \implies 2A = 44 \implies A = 23 if solved as 2A=462A = 46.

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