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 downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

12 : 1
23 : 2
38 : 3
4Cannot be determined

Answer:- 1

Explanation:-

Solution:

Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

\begin{aligned} \Rightarrow (x \times 8 \frac{4}{5}) = (y \times 4) \\ \Rightarrow \frac{44}{5} x = 4 y \\ \Rightarrow y = \frac{11}{5} x \\ ∴ Required ratio \\ = (\frac{y + x}{2}) : (\frac{y - x}{2}) \\ = (\frac{16 x}{5} \times \frac{1}{2}) : (\frac{6 x}{5} \times \frac{1}{2}) \\ = \frac{8}{5} : \frac{3}{5} \\ = 8 : 3 \end{aligned}

$\eqalign{ & \Rightarrow \left( {x \times 8\frac{4}{5}} \right) = \left( {y \times 4} \right) \cr & \Rightarrow \frac{{44}}{5}x = 4y \cr & \Rightarrow y = \frac{{11}}{5}x \cr & \therefore {\text{Required}}\,{\text{ratio}} \cr & = \left( {\frac{{y + x}}{2}} \right):\left( {\frac{{y - x}}{2}} \right) \cr & = \left( {\frac{{16x}}{5} \times \frac{1}{2}} \right):\left( {\frac{{6x}}{5} \times \frac{1}{2}} \right) \cr & = \frac{8}{5}:\frac{3}{5} \cr & = 8:3 \cr}$