Question

The average age of a class of 40 boys is 17 years.but by the admission of a new boy the average is raised 17.05 years.what is the age of the new boy??

Answer 1

As we know,

Average =
$\frac{sum \: of \: object}{total \: number \: of \: object}$
Here,

average age =
$\frac{sum \: of \: ages \: of \: 40 \: students}{number \: of \: total \: students}$
Here,

Average given =
$\frac{sum\:of\:ages\: of\:40\: students}{40}$ = 17

=> sum of ages of 40 students = 40 × 17

=> sum of ages of 40 students = 680

Now if one student is added, average becomes = 17.05

So new average =

$\frac{sum\:of\:ages\:of\:40\:students\:+\:new\: student}{41}$ = 17.05

So,
sum of ages of 40 students + new student = 17.05 × 41

=> sum of ages of 40 students+ new student = 699.05

But, as we calculated above,
sum of ages of 40 students is 680

so,

680 + new student = 682

=> new student = 699.05 - 680 = 19.05

$\boxed{Age\:of\:new\: student\:is\:19.05\:years}$

Hope it helps dear friend ☺️✌️

Answer 2

very easy question

_steps_

1) find the sum of the ages of 40 students

2) find the sum of the ages of 40+1 student

3) subtract EQ 1 from EQ 2