Question

The average age of 30 boys of a class is equal to 14yrs. When the age of the class teacher is included the average becomes 15yrs. The age of the class teacher is

Answer 1

_______________________________

$\textbf\blue{given}$

THE AVERAGE AGE OF STUDENTS :

=> 14 YRS

NO. OF STUDENTS

=> 30

_______________________________

$\textbf{twist }\:$

=> IF AGE OF CLASS TEACHER IS ADDED THE
AVERAGE :

=> 15 YRS

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SEE,

=> AFTER ADDING TEACHER :

=> THERE WERE ALREADY 30 STUDENTS

=> AFTER THIS 1 MORE PERSON IS ADDED

=> NO. OF PEOPLE BECOMES 31

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=> IN SUCH TYPES OF PROBLEMS U NEED TO FIND THE TOTAL ......

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$\textbf{total \: age \: of \: 30 \: students}$

=> AVERAGE AGE OF 30 STUDENTS * NO. OF STUDENTS

=> 14 * 30

=> 420

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$\textbf{total \: age \: of \: studets \: with \: teacher}$

=> AVERAGE OF STUDENTS WITH TEACHER * NO. OF ALL PEOPLE NOW

=> 15 * 31

=> 465

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$\textbf{age \: of \: that \: teacher}$

=> TOTAL AGE OF STUDENTS WITH TEACHER - TOTAL AGE OF STUDENTS

=> 465 - 420

=> 45 YRS

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=> SO AGE OF THE TEACHER :

=> 45YRS

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$\textbf\red{thanks}$

Answer 2

$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,
$\underline{\textit{Statement-1:}}$
The average age of 30 boys of a class = 14yrs.

$\underline{\textit{Statement-2:}}$
When the age of the class teacher is included the average becomes 15yrs.

Age of Class teacher = ? yrs

$\underline{\huge{\textsf{Step-1}}}$
Find the Sum of Ages of 30 boys of the Class

We have,
$\bigstar \mathbf{Average\: of\: n\: observations = \dfrac{Sum\: of\: n\: observations}{No.\: of\: Observations}}$

$\implies \textsf{Sum of n observations = Average of observations \times No. of observations}$

From Statement-1,
$\implies$ Sum of Ages of 30 boys = $14 \times 30$

$\implies \sf \textsf{Sum of Ages of 30 boys = 420}$ ————[1]

$\underline{\huge{\textsf{Step-2}}}$
Note No. of observations when Class teacher is included

No. of observations increases by 1, when Class teacher is included.

No. of Observations = 30 +1
$\implies \sf \textsf{No. of Observations = 31}$————[2]


$\underline{\huge{\textsf{Step-3}}}$
Assume a variable to represent the class teacher's age

Let $\textsf{x}$ be the Age of Class teacher ————[3]


$\underline{\huge{\textsf{Step-4}}}$
Rewrite Statement-2

$\implies$ Average of 30 boys with class teacher's age included = 15 years

$\implies \dfrac{Sum\: of\: the\: Ages\: of\: 30\: boys\: + Class\: teacher's\: Age}{No.\: of\: observations} = 15$

$\underline{\huge{\textsf{Step-5}}}$
Substituting [1], [2], [3]

$\implies \dfrac{x+420}{31} = 15$

$\implies x+420 = 31 \times 15$

$\implies x+420 = 465$

$\implies x = 465 - 420$

$\implies x = 45$


$\therefore$
$\bigstar \textbf{The\: Age\: of\: Class\: teacher = \underline{\mathbf{45\: years}}}$