Since momentum is conserved in the system

Forward momentum of boy = backward momentum of boat

$L$ - Length of boat

$M$ - mass of boat

$t$ - time

$m$ - mass of boy

$x$ - distance moved by boat

$ M(L/t)=(M+m)x/t$

$50 \times 4.5 =(250 +50)x$

$x=0.75\; m$

Hence b is the correct answer.