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Averages Smart Math

[Smart Math] Averages Problem 13

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

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

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

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

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

(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 = \frac{30}{10}=3years. 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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