Question

the average age of 30 students is 9 years if the age of their teacher is included it becomes 10 years ago the age of the teacher in years is

Answer 1

Answer:

Age of the teacher is 40 year.

Step-by-step explanation:

From the properties of average :

• Average = ( sum of quantities ) / ( number of quantities

Given,

Average age of 30 students is 9 year.

= > 9 year = ( sum of ages of 30 students ) / 30

= > 9 x 30 year = sum of ages of 30 students

= > 270 year = sum of ages of 30 students

According to the question : If the age of their teacher is included it becomes 10 years.

= > 10 year = ( sum of ages of students + age of teacher ) / 31

= > 10 x 31 year = 270 year + age of teacher

= > 310 year - 270 year = age of teacher

= > 40 year = age of teacher.

Hence, age of the teacher is 40 year.

Answer 2

Given :------

• Average of 30 boys of class = 9 years .
• After teacher age included new average = 10 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 ..

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Solution :--

it is given that average of 30 boys of class is 9 years.

Putting value in formula we get,

→ 9 = sum of age of all boys /30

(Cross - multiply) we get,

→ sum of age of all boys = 9 × 30 = 270 years..

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Now,

when Age of teacher also included , than Average becomes 10 years .

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

Again,

→ 10 = sum of all members / 31

→ sum of all members = 10×31 = 310 years ..

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Now,

This is the age of 30 students + 1 teacher ,

and , we already have 30 students total age = 270 years.

Hence, Teacher age = 410 - 270 = 40 years ...

So, Age of Teacher was 40 years..

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★ Shortcut ★

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

Here ,

☛ New Average = 10 year

☛ Increased Average = 1 year

☛ Number of students = 30 .

Putting values we get,

➠ Teacher Age = 10 + 1 × 30 = 40 years ..

Hence, Teacher was 40 years old ...

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Similar 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 ...

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