One day at a restaurant there were a total of m workers, consisting of

Question

One day at a restaurant there were a total of m workers, consisting of only waiters and cooks, some of whom had college degrees and others did not. Of these workers n were cooks and 5n/4 had college degrees. If 3n/4 cooks had degrees, m/4 of the waiters did not have degrees and 30 of the workers did not have degrees, how many workers were at the restaurant?

A. 20
B. 40
C. 80
D. 100
E. 120

A. 20
B. 40
C. 80
D. 100
E. 120

chetan2u · Answer

m workers, n cooks and m-n waiters...
(I) 3n/4 cooks had degrees, so n/4 cooks do not have degrees AND m/4 of the waiters did not have degrees.
so n/4+m/4=30....n+m=120....(i)
(II) 5n/4 had college degrees, so m-30 had degrees 
5n/4=m-30....5n=4m-120....(ii)

substitute value of (i)...
5n=4(120-n)-120......5n=480-4n-120......9n=360.....n=40
so m = 120 - 40 = 80
C

let us solve it logically..
30 did not have degrees and from wordings we can say that there are more with degrees than without degrees..
so our answer has to be > 30*2 or >60.
Now from choices available take m as 80..
so m/4 or 80/4 or 20 cooks do not have degree. 
Total 30 did not have degrees, so 30-20 or 10 waiters did not have degrees..
a) 3n/4 cooks had degrees, so n/4 did not have degree, so n/4=10...n=40
b) 5n/4 had college degrees, so 5*40/4=50 had degrees

Total degrees + no degrees = 50+30=80

C

Ofcourse it can be easily done by 2 by 2 matrix.

Archit3110 · Answer

really an amazing question , I solved it using 2x2 matrix..

from the given matrix we can say
m/4+n/4=30
m+n=120
and 2n/4+m/4=m-n
3m=6n
m=2n

solve for m & n we get m= 80 and n=40

IMO C 80 is correct

vinayakvaish · Answer

This is a good but poorly worded question. M/4 of the waiters implies m/4*(m-n) whereas you want to say m/4 waiters. Kindly make this essential correction

rishabhchats · Answer

100% agree. I was solving this for the last 10 minutes and when I saw the solution - I was like nope. Should've been worder "m/4 workers" instead of "m/4 of the workers"/

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One day at a restaurant there were a total of m workers, consisting of

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One day at a restaurant there were a total of m workers, consisting of

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