Question

The average age of 29 boys of a class is 17 years . When the age of the class teacher is included , the average age becomes 18 years . Find the age of the class teacher.

Answer 1

we know that average age = total sum of age of people / number of people

its given that there is 29 boys

the average of 29 boys = (x1 +x2 +....+x29 )/29 = 17 years [where x1 ,x2 denote the respective age of boys ]

if we add teachers age the average age becomes =( x1+....+x29+ X teacher ) /29+1 = 18


x1+x2+........x29 +X /30 = 18 --------------------(1)

WE HAVE (x1 +x2 +....+x29 )/29 = 17

FROM THIS
x1 +x2 +....+x29 = 17*29

apply this in (1)
( 17*29+X ) /30 = 18

solving this

493+X =18*30

x = 540- 493 = 47

therefore age of teacher = 47 years