A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running down stream. The ratio between the speed of the boat and speed of the water current respectively  

Let speed of boat in still water$=x\text{kmph}$

Speed of stream$=y\text{kmph}$

The given information is represent as a table below

$\begin{array}{ccc}& \text{Up}\text{stream}& \text{Down}\text{stream}\\ \text{Distance}& \text{d}& \text{d}\\ \text{Speed}& \text{x-y}& \text{x+y}\\ \text{Time}& \begin{array}{c}\text{8hrs}\text{48mins}\text{.}\\ \left(\text{8}\frac{\text{4}}{\text{5}}\text{hrs}\right)\end{array}& \text{4hrs}\end{array}$

distance$\text{=Time×Speed}$

up stream

$d=8\frac{4}{5}\left(x-y\right)$

$d=\frac{44}{5}\left(x-y\right)$

Down stream

$d=4\left(x+y\right)$

$\frac{44}{5}\left(x-y\right)=4\left(x+y\right)$

$44\left(x-y\right)=20\left(x+y\right)$

$44x-44y=20x+20y$

$44x-20x=20y+44y$

$24x=64y$

$\frac{x}{y}=\frac{64}{24}$

$\therefore \frac{x}{y}=\frac{8}{3}$

$\therefore$ The ratio of boat speed to the current is$8:3$