Question

the average age of a class of 35 student is 14 years. if the teacher's age is included the average age increase by one year. find the age of teacher

Answer 1

35 ×14 =490
it increases 1 year
35++x is 15telangana

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Age of Teacher denoted by m

Sum of age of Students denoted by c

As we know that :-

${\boxed{\sf\:{\dfrac{Sum\;of\;Quantities}{Number\;of\; Quantities}}}}$

Now,

We have the information,

So,

$\textbf{\underline{Average\;age\;of\;class\;of\;35\; students}}$  

= 14 year.

Hence,

Using Formula :-

${\boxed{\sf\:{14=\dfrac{Sum\;of\;age\;of\;35\; Students}{35}}}}$

14 × 35 = c

490 = c

Now,

Given,

If the teacher's age is included

Then,

${\boxed{\sf\:{Average\;age\;increases\;by\;1\;year}}}$

${\boxed{\sf\:{14+1=\dfrac{c+m}{35+1}}}}$

${\boxed{\sf\:{15=\dfrac{490+m}{36}}}}$

15 × 36 = 490 + m

540 = 490 + m

540 - 490 = m

50 = m

Therefore,

Age of the teacher = 50 year