Question

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

Answer 1

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×($1+\frac{1}{4}$)×($1-\frac{1}{3}$) = 100  

X×($\frac{5}{4}$)×($\frac{2}{3}$) = 100  

X×($\frac{10}{12}$) = 100  

X = 100×($\frac{12}{10}$)  

X = 120  

Therefore, the correct option is (b)