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

**Problem**

**Problem**

The average age of 20 boys of a class is 12 years. Ten new boys are admitted and the average age increases by a year. The average age of the new boys is ________ years?

- 13
- 14
- 15
- 16
- 18

**The Usual Method**

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If the average age of 20 boys is 12 years, total age of the 20 boys = 20 x 12 = 240 years.

After admission of 10 new boys, new average age is13 years.

Therefore total age of class = years.

Hence total age of new boys = 390 – 240 = 150 years.

Hence average age of new boys = years.

**(Ans: 3)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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After admission of 10 new students, the total number of students becomes 20 + 10 = 30. If 10 students have to increase the average age by 1 year of 30 students, total increase needed = 1 x 30 = 30 years. This extra 30 years is from 10 students only. Hence extra age per new student = years. Hence average age of the 10 new students = 12 + 3 = 15 years.

**(Ans: 3)**

*Estimated Time to arrive at the answer = 10 seconds.*

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