A $\frac{500}{100}V,$ two$-$winding transformer is rated at $5$ kVA $.$ The following information is available:

A$.$ The maximum efficiency of the transformer occurs when the output of the transformer is $3$ kVA $.$

B$.$ The transformer draws a current of $3$ A $,$ and the power is $100$ W when a $100-V$ supply is impressed on the low$-$voltage winding with the high$-$voltage winding open$-$circuit.

Find the rated efficiency of the transformer at $0\mathrm{.}8$ PF lagging.