how many of the workers have at least 5 but fewer than 10yrs

[vivekjaiswal]

In an office, 40 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?

(A) 48
(B) 64
(C) 50
(D) 144
(E) 160


OA is [spoiler](A)[/spoiler]

Can anyone explain, please.

Cheers,
Vivek.

[Giorgio]

if 16 workers have at least 10 , and 90% fewer than 10 , we can conclude that :

16= 0.1 % of X
X=160 so we have 160 workers total

we know that of these 160 40% or 64 has at least 5 ( which also includes that 16 workers which has at least 10 )

so 160 X 40% - 16= 64 - 16 = 48

Cheers,
Gio

[vivekjaiswal]

if 16 workers have at least 10 , and 90% fewer than 10 , we can conclude that :

16= 0.1 % of X
X=160 so we have 160 workers total

we know that of these 160 40% or 64 has at least 5 ( which also includes that 16 workers which has at least 10 )

so 160 X 40% - 16= 64 - 16 = 48

Cheers,
Gio

Thanks Gio, that clarifies my doubt