When a bullet is fired from a gun, conserved quantity is

When a bullet is fired we get total momentum will be conserved

Note : here conservative quantity means which will remain as it is at every instant

So we get

${\text{P}}_{\text{i}}={\text{P}}_{\text{f}},$  i.e., total momentum before firing = total momentum after firing

${\text{KE}}_{\text{i}}\ne {\text{KE}}_f,$  i.e., total K.E of system before firing $\ne$ total K.E of system after firing

$\Delta {\text{P}}_{\text{B}}=\Delta {\text{P}}_{\text{G}},$  change in momentum of bullet = change in momentum of gun

But this change happen in $\Delta \text{t}$ , so it is not conserved

${\text{F}}_{\text{BG}}=-{\text{F}}_{\text{GB}},$  force exerted by bullet on gun = $-$  force exerted by gun on bullet it also take place in fraction of time$\Delta \text{t}$ , so it is not conserved