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# [Smart Math] Averages Problem 13

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

1. 13
2. 14
3. 15
4. 16
5. 18

### The Usual Method

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 = $13\times \left( 20+10 \right)=390$years.

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

Hence average age of new boys = $\frac{150}{10}=15$years.

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

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 = $\frac{30}{10}=3$years. Hence average age of the 10 new students = 12 + 3 = 15 years.