\(H =\frac{ V ^{2}}{ R } t\)  \(....(i)\)

It is given \(20 \%\) heat is heat to be ejected, thus, the resistance is reduced by \(20 \%\)

The new resistance is,

\(R ^{\prime}= R -0.2 R =0.8 R\)

The new amount of heat generated is,

\(H ^{\prime}=\frac{ V ^{2}}{0.8 R } t ^{\prime}\) \(....(ii)\)

On equating both equations \((i)\) and \((ii)\) we get,

\(\frac{ V ^{2}}{ R } t =\frac{ V ^{2}}{0.8 R } t ^{\prime}\)

\(t ^{\prime}=0.8 \times t =0.8 \times 12 min =9.6 min\)