Question

The average of 30 boys of a class is equal to 15 yrs. When the age of the class teacher is included the average becomes 16 yrs. Find the age of the class teacher.46 yrs

Answer 1

Given :------

• Average of 30 boys of class = 15 years .
• After teacher age included new average = 16 years .
• We have to Find age of Teacher ....

Formula :------

Average is the Mean , Middle value of the number , it is Found by, when we divide all numbers sum by their number ...

Average = sum of observation / Total Number of observation ..

________________________________

it is given that average of 30 boys of class is 15 years.

Putting value in formula we get,

→ 15 = sum of age of all boys /30

(Cross - multiply) we get,

→ sum of age of all boys = 15 × 30 = 450 years..

_________________________________

Now,

when Age of teacher also included , than Average becomes 16 years .

→ Total members now = (30 students + 1 teacher) = 31

Again,

→ 16 = sum of all members / 31

→ sum of all members = 16×31 = 496 years ..

_________________________________

Now,

This is the age of 30 students + 1 teacher ,

and , we already have 30 students total age = 450 years.

Hence, Teacher age = 496 - 450 = 46 years ...

So, Age of Teacher was 46 years..

__________________________________

★ Shortcut ★

→ [[[[ Teacher age = New average + (Increased Average × Number of Students ]]]]

Here ,

☛ New Average = 16 year

☛ Increased Average = 1 year

☛ Number of students = 30 .

Putting values we get,

➠ Teacher Age = 16 + 1 × 30 = 46 years ..

Hence, Teacher was 46 years old ...

___________________________________

#BAL

#answerwithquality

Answer 2

Question:

The average of 30 boys of a class is equal to 15 years. When the age of the class teacher is included the average becomes 16 years. Find the age of the class teacher.

Answer:

Age of the class teacher = 46 years

Note:

Average (or mean) is given as ;

A = (Sum of observations)/(no. of observations)

Solution:

Case1 ;

When the average age of 30 boys was calculated.

Here ,

• Average = 15

• Sum of observations = Sum of ages of 30 boys.

• No. of observations = No. of boys = 30

Since ;

A = (Sum of observations)/(no. of observations)

Thus;

=> 15 = (Sum of ages of 30 boys)/30

=> Sum of ages of 30 boys = 15•30

=> Sum of ages of 30 boys = 450 years ------(1)

Case2 ;

When the age of class teacher was included.

Here,

• Average = 16

• Sum of observations = Sum of ages of 30 boys + Age of the class teacher

• Number of observations = No. of boys + No. of class teacher = (30 + 1) = 31

Since ;

A = (Sum of observations)/(no. of observations)

Thus;

=> 16 = (Sum of ages of 30 boys + Age of the class teacher)/31

=> 16 = (450 + Age of the class teacher)/31

{ using eq-1 }

=> (450 + Age of the class teacher) = 16•31

=> (450 + Age of the class teacher) = 496

=> Age of the class teacher = 496 - 450

=> Age of the class teacher = 46 years

Hence,

Hence,The age of the class teacher is 46 years .