From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000 ?
A. 200
B. 120
C. 100
D. 75
E. 60

Respuesta :

Answer:

Let's assume that "X" be the number of employees in 2000.

∵ it's given :

From 2000 to 2003: the number of employees increased by a factor of 1/4

From 2003 to 2006: the number of employees decreased by a factor of 1/3

∴ We can equate the following details:

X×(increase in employee)×(decrease in employee) = 100

X×([tex]1+\frac{1}{4}[/tex])×([tex]1-\frac{1}{3}[/tex]) = 100  

X×([tex]\frac{5}{4}[/tex])×([tex]\frac{2}{3}[/tex]) = 100  

X×([tex]\frac{10}{12}[/tex]) = 100  

X = 100×([tex]\frac{12}{10}[/tex])  

X = 120  

Therefore, the correct option is (b)

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