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

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+(1)/(4)`)×(
`1-(1)/(3)`) = 100

X×(
`(5)/(4)`)×(
`(2)/(3)`) = 100

X×(
`(10)/(12)`) = 100

X = 100×(
`(12)/(10)`)

X = 120

Therefore, the correct option is (b)