Work done ON something is the opposite of work done BY something. It's similar to a take/give relationship - if you took 5 apples, you gave (-5) apples.
B would imply that no work was done at all.
I may be missing a really basic concept; I think my confusion stems from the use of the phrase "NET WORK." If a net work of 55J is done on the system, doesn't this mean the work done BY the system has already been taken into consideration. if 55J of work is done on the system and 55J of work is done by the system, wouldn't the net work be zero, not 55?