A bullet is fired from a gun with a velocity 600 m/s. The recoil velocity of the gun is 3 m/s. What is the ratio of the mass of the gun and bullet ?

The correct option is C 200:1
Given,

Initially both Gun and bullet will be in rest ie, initial velocity of Gun and bullet $=0$

After fired,

$V_b=600m/s{V}_r=3m/s$

Let mass of gun is $M$ and mass of bullet is $m$.

Using momentum conservation:

Initial momentum (Before fired)$=$ Final momentum (After fired)
$M\times 0+m\times 0=(-3\times M)+600\times m$

$0=-3M+600m$

$\Rightarrow \frac{M}{m}=\frac{600}{3}=\frac{200}{1}$

Ration of mass of Gun to bullet is $\frac{200}{1}$ Option C.