The S$.$C$.$ test on a $1-$phase transformer, with the primary winding short$-$circuited and $30$ V applied to

the secondary gave a wattmeter reading of $60$ W and secondary current of $10$ A$.$ If the normal applied

primary voltage is $200,$ the transformation ratio $1$ :$2$ and the full$-$load secondary current $10$ A$,$ calculate

the secondary terminal p$.$d$.$ at full$-$load current for $($a$)$ unity power factor $($b$)$ power factor $0\mathrm{.}8$ lagging.

If any approximations are made, they must be explained.