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Averages Smart Math

[Smart Math] Averages Problem 6

Here’s and example of a SMART MATH problem for AVERAGES.

Averages

Problem

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

  1. 21.5 years
  2. 22 years
  3. 22.5 years
  4. 23 years
  5. 25 years

The Usual Method

Total age of captain and vice captain = 25 + (25 + 3) = 53 years.

Let the average age of all players be ‘x’ years.

Hence, total age of 11 players = 11x years

11x-53=9(x-1)

\therefore 11x-53=9x-9

\therefore 2x=44

\therefore x=22years

Hence, average age of the whole team = 22 years

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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For 9 players, if the average age goes below by 1 year, the total reduction in age = 9 years. Since, the average age of the 9 players gets reduced due to not including the ages of captain and vice captain. Hence, the captain and vice captain’s age contribute to the reduction of 9 years. Total age of captain and vice captain = 25 + 28 = 53 years.

53 – 9 = 44 years will be the age of 2 players of the team. Hence, average age of the team = \frac{44}{2}=22years

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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