$20$kVA,$\frac{500}{250}V,50Hz,$ single$-$phase transformer gave the following test results $[$S$.$C$.$T test on the HV side:,$40\mathrm{.}5$ V$,35$ A$,500$ W$],[$O$.$C$.$T test on the HV side:,$500$ V$,2$ A$,200$ W$]]$

If the transformer is to operate at an average power factor of $0\mathrm{.}8$ lagging. Determine:

$($a$)$The voltage to circulate full$-$load current in the transformer $($b$)$The efficiency at half$-$load $($c$)$The voltage regulation of the transformer at full$-$load