Work Rate problem

A can complete the job in x hours, therefore A's rate = 1/x
B can complete the job in 1/x hours, therefore B's rate = x

A and B working simultaneously = x+(1/x) = (x^2+1)/x
W/(x^2+1)/x = T

T(x^2+1)/x = W

In y hours A can complete = y/x job.
Now at this point B joins A and they work together for till 100 decks are manufactured.

y/x + W = 100

y/x + [(x^2+1)/x]T =100

[(x^2+1)/x]T =100 - (y/x)
[(x^2+1)/x]T = (100x-y)/x
t = (100x-y)/(x^2+1)

Hence B is the answer.

I know it looks complicated but its not. I was able to do this in less than 1 minute. I find plugging in options very time consuming specially when one can do it easily with variables.

Let me know if you still have any doubts.

Explanations of Chase are perfect, here is how I did:

Number of objects which have to be made by A and B together: (100-y/x)
Number of hours for A and B together to make 1 object: x+(1/x)
Therefore,
(100-y/x) / (x+(1/x)) = 100x - y / x^2 + 1

Thanks very much for the explanations guys!