All employees of Celtic Systems are either programmers or sy

Question

All employees of Celtic Systems are either programmers or systems analysts. On Monday, one programmer was absent, and programmers made up \(\frac{1}{7}\) of the employees present. On Tuesday, two systems analysts were absent, and programmers made up \(\frac{1}{5}\) of the employees present. On Wednesday, two programmers and two systems analysts were absent.

What fraction of the employees present on Wednesday were programmers?

(A) \(\frac{2}{25}\)
(B) \(\frac{1}{10}\)
(C) \(\frac{2}{19}\)
(D) \(\frac{1}{9}\)
(E) \(\frac{1}{8}\)

What fraction of the employees present on Wednesday were programmers?

(A)  \frac{2}{25} 
(B)  \frac{1}{10} 
(C)  \frac{2}{19} 
(D)  \frac{1}{9} 
(E)  \frac{1}{8}

chetan2u · Answer

Let us take programmers to be p and system analysts to be s.

On Monday, one programmer was absent,  and programmers made up  \frac{1}{7}  of the employees present.

So, the number of programmers present is p-1, while total becomes p+s-1.
It is given that p-1=  1/7 ] (p+s-1)
7p-7=p+s-1 or 6p-6=s

Next
 On Tuesday, two systems analysts were absent,  and programmers made up  \frac{1}{5}  of the employees present.
So, the number of programmers present remains p, while total becomes p+s-2.
It is given that p=1/5 (p+s-2)
5p=p+s-2 or 4p+2=s

From the above two equations 
 4p+2=6p-6  or p=4
We can also find s as 4p+2 or 18.

On Wednesday, with two of each absent, the total becomes 4+18-2×2 = 18 while programmer are 4-2 or 2.
 Thus as a fraction of total, programmer are 2/18 or 1/9

adconsectetur · Answer

N = total

P = programmer

Monday: N = 7(P-1) + 1 --> 1 programmer absent
Tuesday: N = 5P + 2 --> 2 analyst absent

P = 4 and N = 22

Wednesday: 2/18 == 1/9

Ans D.

Hope it helps.

vasu1104 · Answer

say total = 100x
programmers =p
analyst = 100x-p

on monday, programmer is absent.
so present programmers = p-1
and present analyst = 100x-p

this present programmers are 1/7 of total present employees.
so total present employees = p-1+100x-p = 100x-1
 so, p - 1 = (1/7) * 100x-1
we get, 100x= 7p-6

now on tuesday , two analyst are absent.
so present analyst= 100x-p-2
present programmers= p

total present all employees= 100x-p-2+p = 100x-2
now the programmers are 1/5 of all present employees.

so, p = (1/5)* (100x-2)
now we know 100x= 7p-6. so from that we can find value of p and then of x.
p= (1/5) *(7p-6-2)
5p = 7p-8
p= 4
so from that we get x=22/100

now total employee= 22
programmers= 4
analyst= 18

on wednesday, 2 of each programmers and anlayst are absent.
so present programmers= 2
present analyst= 16

total present employee= 18

we need programmers proportion on wednesday.
thats 2/18 = 1/9

ans D

All employees of Celtic Systems are either programmers or sy

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All employees of Celtic Systems are either programmers or sy

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