Two transformers, Transformer A$,$ and Transformer B are connected in parallel in a substation. The rating of the two transformers are given in Table $1$ below.

Table $1$ Rated Parameters of Transformer A and Transformer B

$($a$)$ Calculate the impedance of each transformer in ohms referred to the high$-$voltage side and express it in rectangular form.

$($b$)$ If the two transformers supply a total load of $250$ MVA at a power factor of $0\mathrm{.}85$ lagging, calculate the load on each transformer. $($Derive any equations used$).$

$($c$)$ Calculate the efficiency of each transformer assuming the core losses are equal to $\backslash (0\mathrm{.}25\backslash \%\backslash )$ of the rated power for each transformer.