Given: The mass of shell is , mass of gun is and the muzzle speed of the shell is .
Initially, both the gun and the shell are at rest therefore, the initial momentum of the system is zero.
The final momentum of the system is given as,
Where, is the mass of shell, is the mass of gun, is the velocity of shell and is the recoil velocity of gun.
From the conservation of momentum,
By substituting the given values in the above equation, we get
Thus, the recoil velocity of gun is .