$46$ A $\backslash (110-\backslash$mathrm$\{$kVA$\},1\backslash )-$phase transformer has a ratio of $\backslash (11000/440\backslash$mathrm$\{$~V$\}\backslash ).$ The iron loss measured on open$-$circuit is $1100$ W $.$ With the secondary winding short$-$circuited, a voltage of $500$ V at normal frequency applied to the primary produces full$-$load current, the wattmeter reading $1000$ W $.$ Calculate $($a$)$ the secondary terminal voltage, $($b$)$ the efficiency, when a current of $250$ A at a lagging power factor of $0\mathrm{.}8$ is taken by a load connected to the low$-$voltage terminals, the primary voltage being $11000$ V $.$

$[($a$)425$ V ; $($b$)\backslash (97\backslash$cdot $6\backslash \%\backslash ).]$