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### MATHS TRICK - APPLICATION LEVEL

? The average of 30 students in a class is 14 years. When age of class teacher is included the average becomes 15 years. Find the age of class teacher.

Solution :

Conventional method

No of students = 30

Average age = 14

Sum of age = 30 x 14 = 420

Total people including teacher = 31

Average age = 15

Sum of age = 31 x 15 = 465

Teachers age is 465- 420 = 45

No need for any formula… Use simple common sense

You all know that average means total sum divided by number of person/items etc..

Here, the number of students = 30

When teacher is included total persons = 31

Average of 30 students = 14

Let us assume that age of class teacher is also 14 yrs

Now, average of 31 persons is 14 itself (note: average is unaffected )

But common sense says class teacher cannot be of the age 14 years.

He or she should be more than 14 years.

How many years more?

Now come to the question …it says the average becomes 15.

It means 1 year more.

Or, 1 year should be added to all the 31 people’s age ( including teacher)

Therefore 1×31 =31

So, the class teacher is not of 14 years but his/her age is 31 years more.

14+ 31 = 45

Confused ?

Let me give more simple steps:-

Don’t worry, all you have to do is just check how much average has increased. …in this case 1.
Multiply it by total number of persons (here, including teacher)….in this case 1×31.
Add this to the earlier average….. in this case 14+31 = 45