Question

the average age of 30 boys of a class is equal to 14 years when the age of the class teacher is included, the average becomes 15 years . find the age of the class teacher ?

Answer 1

Sum of Total age without teacher = 30 * 14 = 420 yrs.

Sum of total age including teacher = 31 * 15 = 465 yrs.

So age of teacher = 465 yrs. - 420 yrs. = 45 yrs.

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Answer 2

Given:

The average age of 30 boys of a class = 14yrs.

When the age of the class teacher is included the average becomes 15yrs.

To Find:

The age of the class teacher

Solution:

We know that,

Average of n number of observations = Sum of all the observations / n

Let the sum of all the ages of boys be y and the age of the class teacher  be x

According to the question,

y / 30 = 14      - (1)

and

y + x / 31 = 15     - (2)

(Total number of observations increases by one because the age of teacher is also added)

From equation 1,

y = 14 X 30

= 420

Substituting the value of y in equation 2,

420 + x = 15 X 31

or x = 465 - 420

= 45

Hence, the age of the class teacher is 45 years.