Question

A sailor goes 8km downstream in 40 minutes and returns in 1 hour. Determine the speed of the sailor in still water and the speed of the current.
A.Speed of sailor = $12km/hr$ & speed of current = $4km/hr$
B.Speed of sailor = $16km/hr$ & speed of current = $7km/hr$
C.Speed of sailor = $10km/hr$ & speed of current = $2km/hr$
D.Speed of sailor = $16km/hr$ & speed of current = $9km/hr$

Answer 1

Hint- There is a variety of sub concepts which are related to answering questions based on boat and streams. Here first of all we have to learn all the terms which are important to understand to understand the concept of streams, and finally we will solve this numerical problem with the help of this concept.

Complete step-by-step answer:
Stream- The flowing water in the river is known as stream.
Upstream- If we go against the direction of the stream, then we are going upstream. The net speed of the boat is called upstream speed.
Downstream- If we go in the direction or with the flow of the river, then we are going downstream. The net speed of the boat is called downstream speed.
Still water- When the speed of the stream is zero i.e. in pond or lakes
Formula used
Let u be the speed of the boat in the still water and v be the speed of the stream.
Upstream = $\left( {u - v} \right)km/hr$
Downstream = $\left( {u + v} \right)km/hr$
Given
Distance the sailor covers = 8km
Time taken to go downstream = 40 minutes
Time taken to go upstream = 1 hour
Let the speed of the boat in still water be x
And the speed of the stream be y=$x - y$
Speed of the sailor in downstream = \[x + y\]
Speed of the sailor in upstream =
As we know, ${\text{distance = speed }} \times {\text{ time}}$
When the sailor is going downstream
Distance is 8 km, time is 40 minutes
$
  {\text{distance = speed }} \times {\text{ time}} \\
   \Rightarrow {\text{8 = }}\left( {x + y} \right) \times \dfrac{{40}}{{60}} \\
   \Rightarrow 24 = 2\left( {x + y} \right) \\
   \Rightarrow x + y = 12..........\left( 1 \right) \\
 $
When the sailor is going upstream
Distance is 8 km, time is 1 hour
$
  {\text{distance = speed }} \times {\text{ time}} \\
   \Rightarrow {\text{8 = }}\left( {x - y} \right) \times 1 \\
   \Rightarrow x - y = 8..........\left( 2 \right) \\
$
Now, adding equation (1) and (2), we get
$
   \Rightarrow x + y + x - y = 12 + 8 \\
   \Rightarrow 2x = 20 \\
   \Rightarrow x = 10km/hr \\
$
Speed of the sailor is $10km/hr$
From equation (1)
$
   \Rightarrow x + y = 12 \\
   \Rightarrow 10 + y = 12 \\
   \Rightarrow y = 2km/hr \\
$
Speed of the current is $2km/hr$
Hence, the correct option is C.

Note- In order to solve these types of questions, the first thing is to learn the concept of upstream and downstream as we mentioned above. After that extract the information from the question and frame the equations. Solve the equations step by step. And remember the basic relation between speed, time and distance.