Question

the mean age is 30 students is 9 years if the age of teacher is included then mean becomes 10 years what is the age of the teacher​

Answer 1

HEY MATE :

given here .

mean of 30 student = 9 years .

and

include age of teacher mean becomes = 10 year.

late

x= sum of age 30 students

x/ 30=9

x= 270.

y= age of teacher .

a/c to question..

(x+y)/31=10

(270+y)/31=10

270+y= 310

y= 310-270

y=40.

thus:

age of teacher :

40 years.

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The age of Teacher is 40 years.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Mean age of 30 students = 9 years

If the teacher's age is added mean = 10 years

To find :

The age of the teacher

Solution :

First, find the total sum of the ages of the students.

Consider the total ages as x

★ We know that :

$\boxed{\sf{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\tt{\implies} \: 9 = \dfrac{x}{30}$

$\tt{\implies} \: 9 \times 30 = x$

$\tt{\implies} \:x = 270$

The total Sum of ages of the students is 270 years.

If the age of teacher is added, new mean is 10 years.

Consider the age of teacher as y

$\tt{\implies} \:10 = \dfrac{270 + y}{31}$

$\tt{\implies} \:10 \times 31 = 270 + y$

$\tt{\implies} \:310 = 270 + y$

$\tt{\implies} \:y = 310 - 270$

$\tt{\implies} \:y = 40$

$\therefore$ The age of Teacher is 40 years.

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\tt{\implies} \:10 = \dfrac{270 + 40}{31}$

$\tt{\implies} \:10 = \dfrac{310}{31}$

$\tt{\implies} \:10 = 10$

$\therefore$ The age of Teacher is 40 years.