Question

the average age of a class of 25 students is 15 years if the age of teachers is added then their average becomes 16 years find the age of teacher​

Answer 1

We need to recall the following definition of an average.

Average is the ratio of the sum of all numbers to the total number of numbers.

Given:

The average age of $25$ student's $=15$ years

The average age of $25$ students and a teacher $=16$ years

Let $S$ be the sum of the age of all students.

Let  $T$ be the age of the teacher.

From the definition of average, we get

$\frac{S}{25}=15$

$S=25*15$

$S=375$

The average age of students and the teacher is,

$\frac{375+T}{26}=16$

$375+T=26*16$

$375+T=416$

$T=416-375$

$T=41$

Hence, the age of the teacher is $41$ years.

Answer 2

Given: Total number of students in the class = 25

           Average age of the students = 15 years

           Average age, if the age of teacher is added = 16 years

To find: The age of teacher

Let: The age of teacher be $x$

Solution: According to the given question,

Total number of students ( N ) = 25

Mean ( $\bar{X}$ ) = 15 years

Total value of ages of students ( ∑X ) = ?

∵ $Mean (\bar{X}) = \frac{Total \ value \ of \ items}{Number \ of \ items}$

∴ ∑X =  $\bar{X}$ * N

∴Total value of ages of students ( ∑X ) = 15 * 25 = 375

Now, if age of teacher is added, then ∑X = $375 + x$

and number of people (N) = 25 + 1 = 26

∵ $\bar{X}$ = $\frac{375 \ + \ x}{26}$ = 16   [given]

⇒ $375 + x = 16 \ * \ 26 = 416$

⇒ $x = 416 - 375 = 41$

Hence, age of teacher is 41 years.