==> $K = \frac{1}{2}$
Again $\frac{{60 - 50}}{t} = \frac{1}{2}\left( {\frac{{60 + 50}}{2} - 30} \right)$
==> $t = 0.8 \times 60 = 48$sec.
$(i)$ The maximum intensity of the emitted radiation will occur at frequency $v /3$
$(ii)$ The maximum intensity of the emitted radiation will occur at frequency $3v $
$(iii)$ The total energy of emitted radiation will become $81\,E$
$(iv)$ The total energy of emitted radiation will become $27\,E$
$Reason :$ Peak emission wavelengths of a black body is proportional to the fourth-power of temperature.