Question

In a class, the mean of age of 75 students is 7 years. If the mean of their ages along with their age, the age of their class teacher is 7.5 years. What is the age of class teacher in years ?



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Answer 1

AnswEr :

• Mean Age of 75 Students = 7 years
• If Age of Class Teacher is included then, it will be 7.5 years
• Find the Age of Class Teacher.

$\bigstar \:\boxed{\textsf{Total Age = Mean \times Number of Students}}$

$\rule{100}{2}$

• Total Age of Students in the Class :

↠ Total Age = Mean × Number of Students

↠ Total Age = 7 years × 75

↠ Total Age = 525 years

$\rule{200}{1}$

• Now Age of Class Teacher will be :

$\longrightarrow \tt Total \:Age_{(Teacher+Students)} = Mean \times Total \:Number \\\\\\\longrightarrow \tt (Teacher \:Age+ 525)=7.5 \times(75 + 1) \\\\\\\longrightarrow \tt (Teacher \:Age+525)=7.5 \times76 \\\\\\\longrightarrow \tt (Teacher \:Age+ 525)= \dfrac{75}{10} \times 76 \\\\\\\longrightarrow \tt (Teacher \:Age+ 525)=\dfrac{570 \cancel0}{1\cancel0} \\\\\\\longrightarrow \tt (Teacher \:Age+ 525)=570 \\\\\\\longrightarrow \tt Teacher \:Age=(570 - 525) \:years \\\\\\\longrightarrow \boxed{ \red{\tt Teacher \:Age=45 \:years}}$

⠀

∴ Age of the Class Teacher is 45 years.

Answer 2

$\bf{\Huge{\boxed{\sf{\green{ANSWER\::}}}}}}}$

$\bf{\Large{\underline{\tt{Given\::}}}}}}$

In a class, the mean of age of 75 students is 7 years. If the mean of their ages along with their age, the age of their class teacher is 7.5 years.

$\bf{\Large{\underline{\bf{To\:find\::}}}}}$

The age of class teacher in years.

$\bf{\Large{\underline{\sf{\pink{Explanation\::}}}}}}$

Let the age of 75 students be R1,R2,R3...........,R75.

We now that formula of the mean;

$\leadsto\bf{\Large{\boxed{\sf{Mean=\frac{Sum\:of\:all\:data}{Number\: of \:data} }}}}$

Therefore,

$\longmapsto\sf{7=\frac{R1+R2+R3..........+R75}{75} }$

$\longmapsto\sf{R1+R2+R3.........+R75\:=\:525}$

We have total student's is 525.

Again,

$\longmapsto\sf{7.5=\frac{Teacher's\:age+525}{76} }}$

$\longmapsto\sf{7.5*76=Teacher's\:age+525}$

$\longmapsto\sf{570=Teacher's\:age+525}$

$\longmapsto\sf{Teacher's\:age=570-525}$

$\longmapsto\sf{Teacher's\:age=45\:years}$

Thus,

$\bf{\large{\boxed{\tt{\pink{The\:age\:of\:teacher\:is\:45\:years.}}}}}}$