Question

The average age of a class of 29 students is 20 years. If the age of teacher is included, then the average increases by 3 months. Find the age of the teacher.
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Answer 1

Answer:

27 Years 6 Months

Step-by-step explanation:

Let Age Of Teacher Be X

Average Age Of Students = 29           {Given}

Total Students = 20                              {Given}

Hence, Total Age Of Students = 29 * 20 = 580

Average Class Of Age After Including Teacher = 20.25     {Given}

= ( Total Age Of Students + Age Of Teacher )  / Total Number Of People

= ( 580 + x ) / 30

20.25 * 30 = 580 + x

X = 27.5 ( 27 Years And 6 Months )

Answer 2

Step-by-step explanation:

Given that:The average age of a class of 29 students is 20 years. If the age of teacher is included, then the average increases by 3 months.

To find:Age of the teacher

Solution: We know that mean/average is given by

$\bar{x}=\frac{\Sigma\:x_i}{f_i}\\\\\bar{x}=\frac{Sum\:of\:all\: observation}{Total\: observation}$

So,ATQ

$20=\frac{Sum\:of\:all\: observation}{29}\\\\Sum\:of\:ages\: of\: students=20\times29\\\\Sum\:of\:ages\: of\: students=580\:years$

Now,including teacher; Total observation=29+1=30

New average= 20 years 3 months= 20.25 years

$20.25=\frac{Sum\:of\:all\: observation}{30}\\\\Sum\:of\:ages\: of\: students\:and\:teacher=20. 25\times30\\\\Sum\:of\:ages\: of\: students\:and\:teacher=607.5\:years$

Age of teacher= Sum of ages of teacher and student-sum of ages of students

Age of teacher=607.5-580

Age of teacher=27.5 years= 27 years 6 months.

Hope it helps you.