Q$6.$d$)$ The short$-$circuit tests on two single phase transformers gave the following results:

$200$kVA:$3\%$ rated voltage; rated current at $0\mathrm{.}25$ p$.$f$.$ lag.

$500$kVA:$4\%$ rated voltage; rated current at $0\mathrm{.}3$ p$.$f$.$ lag.

These two transformers are connected in parallel. How do they share a load of $800$ KW at $0\mathrm{.}85$ p$.$f$.$ lag?

A single phase two winding $220$kVA,$\frac{2000}{200}V$ transformer is to be used an auto$-$transformer for stepping up the voltage from $2000$ V to $2400$ V $.$ At rated load, the two$-$winding transformer has $2\mathrm{.}5\%$ loss, $3\mathrm{.}5\%$ voltage regulation and $4\mathrm{.}5\%$ impendence. Determine the following for the auto$-$transformer:

$($i$)$ voltage and current rating $($ii$)$ kVA rating $($iii$)$ efficiency