Finding expenditure: What was the initial expenditure (in Rs) of company?

[Priya25]

A company, at the time of inflation reduced the staff in the ratio 5 : 3 and average salary per employee is increased in the ratio 7 : 8. By doing so, the company saved Rs 55000. What was the initial expenditure (in Rs) of company?

1) 155000
2) 160000
3) 175000
4) 215000

 

[stapel]

A company, at the time of inflation reduced the staff in the ratio 5 : 3 and average salary per employee is increased in the ratio 7 : 8. By doing so, the company saved Rs 55000. What was the initial expenditure (in Rs) of company?

1) 155000
2) 160000
3) 175000
4) 215000

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please reply with a clear listing of your thoughts and efforts so far. Thank you!

 

[HallsofIvy]

Let N be the original number of employees and P the original average salary. Then the original cost was NP. After the employees were "reduced in ratio 5:3" there were (3/5)N employees. After the average salary was "increased in the ratio 7 : 8" the average salary was (8/7)P. The new cost was (3/5)N(8/7)P= (24/35)NP. "By doing so, the company saved Rs 55000" so NP- (24/35)NP= (11/35)NP= 55000. So NP= (55000)(35/11).