[Smart Math] AVERAGES PROBLEM 5

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

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?

1. 12.1 years
2. 12.4 years
3. 12.3 years
4. 12.5 years
5. 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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