Since Machine A can complete the job in 'x' hours, the job completed by Machine A in 1 hour will be 1/x

Similarly, since Machine B completes the job in 'y' hours, Machine B will complete 1/y of the job in 1 hour

Hence the job completed in 1 hour when A and B work together at their respective rates is:

1/x + 1/y = (x+y)/xy

Since A completes 1/x of this job, 1/x of the total job is what Machine B will not have to complete because of Machine A's help.

So, the required quantity is (1/x) of (x+y)/xy i.e. (1/x)/(x+y)/xy = xy/x(x+y) = y/(x+y)

Hence, in my opinion, the answer should be

option E.

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MBA Candidate 2015 | Georgetown University

McDonough School of Business