Question

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?
A. 2:1
B. 3:2
C. 8:3
D. Cannot be determined
E. None of these

Answer 1

Hint: We will take the boat's upstream speed as x km/h and downstream speed as y km/hr. Then, we will use the relation between time, speed and distance, given by
$time=\dfrac{\text{speed}}{\text{distance}}$
We will equate the distance covered for both upstream and downstream to get a relation. Then, we will find the ratio, substitute the obtained relation in it to get the final answer.

Complete step-by-step solution:
In this question, we need to compare the distance covered in upstream to the distance covered in downstream. i.e. we need to find the ratio of the distances.
Let us take the boat's rate upstream to be x km per hour and downstream to be y km per hour.
Then, we can write that the distance covered upstream in 8 hours 48 min = distance covered downstream in 4 hours.
So, by distance-time formula, we have
$\begin{align}
  & \Rightarrow x\times 8\dfrac{4}{5}=y\times 4 \\
 & \Rightarrow x\times \dfrac{44}{5}=y\times 4 \\
 & \Rightarrow \dfrac{44}{5}x=4y \\
 & \Rightarrow y=\dfrac{11}{5}x..........(i) \\
\end{align}$
As asked in the question we need to find the ratio of speed of boat to the speed of current.
Now, we will make a ratio of speed of boat to the speed of current i.e.
$\Rightarrow $ Speed of boat : speed of current
Therefore, we get the required ratio is:
$\Rightarrow \dfrac{y+x}{2}:\dfrac{y-x}{2}$
Using equation (i), we have
$\begin{align}
& \Rightarrow \left( \dfrac{16x}{5}\times \dfrac{1}{2} \right):\left( \dfrac{6x}{5}\times \dfrac{1}{2} \right) \\
 & \Rightarrow \dfrac{8x}{5}:\dfrac{3x}{5} \\
\end{align}$
$\Rightarrow $ x and 5 will be cancelled.
$\Rightarrow $ 8:3
So, the correct option is C i.e. 8:3.

Note: You should know how to form equations or compare the equations. Mistakes can be made when we calculate downstream and upstream ratio wrong as $\dfrac{y-x}{2}:\dfrac{y+x}{2}$ or some other areas where calculation or concept could go wrong. In upstream downstream questions, always distance-time formulae are used. First understand the question and then you will get to know the flow of the question.