Math Problem:Please Help

[alaynaik]

19. 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

[sk818020]

90% of the office has less than 10 years of service and 16 workers have 10 years or greater. Those 16 are the 10% that have worked 10 years or greater. Thus,

10/100=16/x
1/10=16/x
x=160

So the total work force is 160.

We also know that 40% of the workers have 5 years or greater and we know that 16 have 10 years or greater thus;

(40/100)*160 - 16 = Those with at least 5 but fewer than 10 years of service.

(4/10)*160 - 16 = 4*16 - 16 = 64 - 16 = 48

The answer is option A.

[clock60]

19. 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

the same option with double matrix

__________ at least 5_________fewer 5______total

at least 10___ (16)_____________ (0)__________16

fewer 10_____(48)_____________(96)_______0,9x (144)

total_______ 0,4x (64)________ 0,6x( 96)_____ x (160)

in the brakets there are values that are obtained while solving
the answer is 48

[indiantiger]

let T be the total number of workers
40% of workers have at least 5 years of experience

16 workers have at least 10 years of experience

90% of workers have fewer than 10 years of experience this can also be translated to 10% have experience of 10 or more than 10 years
this gives us 10%T = 16 or (1/10)* T = 16
T= 160

Now 40% of T = (40/100) *160 = 64 workers have experience greater than 5 years
but we want workers with experience between 5 and 10 years
so 64 -16(workers with at least 10 years of experience) = 48(A)