Calculating the New Average Age of HR Department

[matrixone]

Homework Statement

There are 100 employees in an organization across five departments. The following table gives the department-wise distribution of average age, average basic pay and allowances. The gross pay of an employee is the sum of his/her basic pay and allowances.

There are limited number of employees considered for transfer/promotion across departments. Whenever a person is transferred/promoted from a department of lower average age to a department of higher average age, he/she will get an additional allowance of 10% of basic pay over and above his/her current allowance. There will not be any change in pay structure if a person is transferred/promoted from a department with higher average age to a department with lower average age.

There was a mutual transfer of an employee between Marketing and Finance departments and transfer of one employee from Marketing to HR. As a result the average age of Finance department increased by one year and that of Marketing department remained the same. What is the new average age of HR department?

1. 30
2. 35
3. 40
4. 45
5. cannot be determined

Homework Equations

The Attempt at a Solution

these are the equations i came up with .

$\frac{m_1 + m_2 + ... + m_{30}}{30}=35...(1)$

$\frac{f_1 + f_2 + ... + f_{20}}{20}=30...(2)$

$\frac{h_1 + h_2 + ... + h_5}{5}=45...(3)$

$\frac{f_1 + m_3 + ... + m_{30}}{29}=35...(4)$

$\frac{m_1 + f_2 + ... + f_{20}}{20}=31...(5)$

$\frac{h_1 + h_2 + ... + h_5 + m_2}{6}= ? ...(6)$

using (3) in (6) i get

$\frac{45*5+m_2}{6}= ?$

So, if i find $m_2$ , i have the answer.

But can't find a way to do that. :(

 

[haruspex]

A simpler notation might help. Writing M, H etc. for the initial sums of ages
M=30*35
M-m₁-m₂+f₁=29*35
Etc.
At first blush, it seems as though you have two equations but three unknowns. But maybe for two of the unknowns it is only the difference between them that matters.