Here, the mass of gun, $M=100\mathrm{ }\mathrm{kg}$

Mass of shell, $m=0.02\mathrm{ }\mathrm{kg}$

Speed of shell, $v= 80\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ and let recoil speed of the gun $=V$

$\therefore$ Speed of shell $=v+V$

As initially both the gun and the shell are the rest before firing, so the initial momentum $\left(P_i\right)$ of the system = 0

Final momentum $\left(P_f\right)$ of the system after firing

$=MV+mv=100V+0.02\times \left(80+V\right)$

According to the law of conservation of linear momentum,

$P_i=P_f$

$0=100 V+1.6+0.02V$

$\Rightarrow V\approx \frac{-1.6}{100}=0.016\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$

$\therefore$ Recoil speed of gun, $V=0.016 \mathrm{m} {\mathrm{s}}^{-1}=1.6\mathrm{ }\mathrm{cm} {\mathrm{s}}^{-1}$