Velocity of a rocket at any time $t$,
$v=u\left(\frac{m_{0}}{m}\right)-gt$
where, $u=$ speed of exhausted gases,
$m_{0}=$ initial mass of the rocket
and $m=$ mass of the rocket at time $t$
Given, fuel burned rate, $\left(\frac{d m}{d t}\right)=100 \,kg / s , u=5\,km / s$
Then, $v=5 \ln \left(\frac{m_{0}}{m}\right)-g t$
As, it is given that the gravitational force is ignored and mass of rocket is reduced to $\frac{1}{20}$ th of it's initial mass i.e, $m=\frac{1}{20} m_{0}$.
or $ \frac{m_{0}}{m}=20$
So, $v=5 \ln (20)\, km / s$