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.
