Here’s and example of a **SMART MATH** problem for **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?

- 21.5 years
- 22 years
- 22.5 years
- 23 years
- 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 = 11*x* years

years

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 = years

**(Ans: 2)**

*Estimated Time to arrive at the answer = 15 seconds.*

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