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

**Problem**

**Problem**

The average age of 40 boys of a class is 12 years. When 10 new boys are admitted, the average is increased by 0.1 year. What is the average age of the new boys?

- 12.1 years
- 12.4 years
- 12.3 years
- 12.5 years
- 13.0 years

**The Usual Method**

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If the average age of 40 boys = 12 years, total age = 40 x 12 = 480 years

With 10 new boys, total number of boys = 40 + 10 = 50

New average = 12.1 years.

Hence, new total age = 50 x 12.1 = 605 years

Hence, total new age added by the 10 new boys = 605 – 480 = 125 years.

Hence, average age of the 10 new boys = = 12.5 years.

**(Ans: 4)**

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

**Using Technique**

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The average age has increased by 0.1 years with 50 boys. Hence, total increase = 0.1 x 50 = 5 years. This 5 years increase is due to 10 boys, so additional age over the normal average age of 12 years is = 0.5 years.

Hence, average age of new boys = 12 + 0.5 = 12.5 years

**(Ans: 4)**

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

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