Question

the average age of 30 students is 16 years. if the age of the teacher is also included then the average age increased by 1 year, find the age of the teacher. select one: a. 47 year b. 45 year c. 49 year d. 46 year

Answer 1

1. Given the average age of 30 students is 16 years i.e, (x1+x2+.....x30)/30=16
2. (x1+x2+.....x30)=480
3. if the age of the teacher is also included then the average age increased by 1 year i.e,(x1+x2+.....x31)/31=17(****here x31 is age of teacher****)
4. (x1+x2+.....x31)=527
5. i.e,x1+x2+...........+x30+x31=527
6. x31=527-480
7. x31=47
8. hence age of teacher is 47 years

Answer 2

The age of the teacher is 47 years and option(a) is correct.

Step-by-step explanation:

Given:

The average age of 30 students is 16 years.

When the age of the teacher is included then the average age  is   increased by 1 year.

To Find:

The age of the teacher.

Solution:

As given,the average age of 30 students is 16 years.

P=30

The average age of 30 students = 16 years.

$The\ average\ age\ of\ 30\ students= \frac{Total\ of\ age\ of\ 30\ students}{Total\ of \age\ of\ students}$

                                                $16= \frac{Total\ of\ age\ of\ 30\ students}{30}$

      $Total\ of\ age\ of\ 30\ students= 16\times30=480$

As given. when the age of the teacher is included then the average age  is   increased by 1 year.

The average age of 30 students +teacher  = 17 years.

The no. of students and teacher in a class =31

$The\ average\ age\ of ( 30\ students +teacher)= \frac{Total\ of\ age\ of( 30\ students +teacher)}{Total\ of \age\ of\ students +teacher}$

                                                               $17= \frac{Total\ of\ age\ of( 30\ students +teacher)}{31}$

$Total\ of\ age\ of(30\ students+teacher)= 17\times31=527$

The age of the teacher=Total of age of (30  students +teacher) - Total of age of 30  students

                                      $=527-480\\=47\ years$

Thus,the age of the teacher is 47 years and option(a) is correct.

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