Question

1. The average age of a class of 35 students is 14 years. If the teacher's age is included,
the average age increases by one year. Find the age of the teacher.​

Answer 1

Answer:

Age of the teacher is 50 year.

Step-by-step explanation:

From the properties of average :

• Average = Sum of quantities / number of quantities

Here, average age of a class of 35 students is 14 year.

= > 14 = ( sum of ages of 35 students ) / 35

= > 14 x 35 = sum of ages of 35 students

= > 490 = sum of ages of 35 students

According to the question : If the teacher's age is included, the average age increases by one year.

= > 14 + 1 = ( sum of ages of students + age of teacher ) / ( 35 + 1 )

= > 15 = ( 490 + age of teacher ) / 36

= > 15 x 36 = 490 = age of teacher

= > 540 - 490 = age of teacher

= > 50 = age of teacher

Hence, age of the teacher is 50 year.

Answer 2

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

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

The average age of a class of 35 students is 14 years. If the the teacher's age is include, the average age increases by one 1 year.

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

The age of the teacher.

$\bf{\Large{\underline{\tt{\green{Explanation\::}}}}}$

We know that formula of the average,we get;

$\leadsto\tt{Average\:=\:\frac{(a1+a2+a3..............+an)}{n}}$

So,

$\longmapsto\sf{Average\:=\:\frac{R1+R2+R3................+R35}{35} =14}$

$\longmapsto\sf{Average\:=\:R1+R2+R3.............+R35=14*35}$

$\longmapsto\sf{Average\:=\:R1+R2+R3.............+R35=490}$

$\mapsto\rm{\orange{New\:average\:=\:14+1=15}}$

$\longmapsto\sf{New\:average\:=\:\frac{(R1+R2+R3............+R35)+R}{36} =15}$

$\longmapsto\sf{New\:average\:=\:\frac{490+R}{36} =15}$

$\longmapsto\sf{New\:average\:=\:490+R=15*36}$

$\longmapsto\sf{New\:average\:=\:490+R=540}$

$\longmapsto\sf{New\:average\:=\:R=540-490}$

$\longmapsto\sf{\orange{New\:average\:=\:R\:=50\:years}}$

Thus,

The age of the teacher is 50 years.