Question

In AIT, all lecturers are either in a full time faculty or a part time faculty. There are more than twice as many lecturers in full time faculty as in part time faculty. The arithmetic mean salary is $25000 for the full time faculty and $35000 for the part time faculty. What do you think could be the average salary for all of the faculty? What if there were exactly twice as many lecturers in full time faculty as in part time faculty?

Answer 1

Given :

There are more than twice as many lecturers in full time faculty as in part time faculty

The arithmetic mean salary for the full time faculty = $25000

The arithmetic mean salary for the part time faculty = $35000

To Find :

The average salary for all of the faculty

Solution :

Let The number of lecturers in part time = p

Let t=The number of lecturers in full time = f

So,

According to question

    f  = 2 p

Arithmetic mean salary for the full time faculty = $\dfrac{f_1+ f_2+f_3+..........+f_n}{n}$

i.e   $\dfrac{f_1+ f_2+f_3+..........+f_n}{n}$ = 25000

Or, $f_1+f_2+f_3+...........+f_n$ = 25000 n

And

Arithmetic mean salary for the part time faculty = $\dfrac{p_1+ p_2+p_3+..........+p_m}{m}$

i.e  $\dfrac{p_1+ p_2+p_3+..........+p_m}{m}$  = 35000

Or, $p_1+p_2+p_3+..........+p_m$ = 35000 m

Since

    f = 2 p

So,   $f_1+f_2+f_3+...........+f_n$ = 2 ( $p_1+p_2+p_3+..........+p_m$ )

or,   25000 n = 2 × 35000 m

o,   25 n = 2 × 35 m

Or,  5 n = 14 m

Or,     n = $\dfrac{14 m}{5}$

Again

The average salary of all faculty = $\dfrac{p_1+p_2+p_3+.........+p_n + f_1+f_2+f_3+..........+f_m}{n+m}$

 =  $\dfrac{25000n+35000m}{n+m}$

 =  $\dfrac{25000\times \dfrac{14m}{5}+35000m}{\dfrac{14m}{5}+m}$

 = $\dfrac{350000m+35000m}{14m+5m}$

 = $\dfrac{385000m}{19m}$

 = 20263.15

Hence, The average salary of all faculty is Rs 20263.15   Answer