Question

A man can row 5 kmph in still water. If the river is running at 1kmph, it takes 75min to go to a place and come back. How far is the place?
A. 2.5 km
B. 3 km
C. 4 km
D. 5 km

Answer 1

Hint: Here in this question, we have to find the distance covered by the man in still water. To solve this, Let us take a distance covered by a man is x and by using a concept of boat and stream concept identify the upstream and downstream speed of man and further simplify by using a basic arithmetic operation we get the required distance covered by man.

Complete step-by-step answer:
To solve this, we know the simple formula:
Upstream = \[\left( {u - v} \right)\] kmph,
Downstream = \[\left( {u + v} \right)\] kmph,
where “u” is the speed of the man in still water and “v” is the speed of the stream or river.
Now, consider the question:
A man can row at speed of 5 kmph in still water i.e., \[u = 5\,kmph\]
The river running at speed of 1 kmph. i.e., \[v = 1\,kmph\]
The man taken 75 mins to go to a place and come back in river, we have to find the distance covered by man.
Let us take the distance to the place covered by man be \[x\,km\].
Speed upstream = \[\left( {5 - 1} \right)\, = 4\,kmph\]
Speed downstream = \[\left( {5 + 1} \right)\, = 6\,kmph\]
As we know, the relation between distance-speed and time is: \[Speed = \dfrac{{distance}}{{time}}\] or\[time = \dfrac{{distance}}{{speed}}\].
Given the time to cover the distance is \[75kmph = \dfrac{{75}}{{60}}\], then
\[ \Rightarrow \,\,\dfrac{x}{4} + \dfrac{x}{6} = \dfrac{{75}}{{60}}\]
Take 12 as LCM in LHS, then
\[ \Rightarrow \,\,\dfrac{{3x + 2x}}{{12}} = \dfrac{{75}}{{60}}\]
Divide both numerator and denominator of RHS by 3, then
\[ \Rightarrow \,\,\dfrac{{5x}}{{12}} = \dfrac{{25}}{{20}}\]
On cross multiplication. We have
\[ \Rightarrow \,\,5x \times 20 = 25 \times 12\]
\[ \Rightarrow \,\,100x = 300\]
Divide both side by 100, then
\[ \Rightarrow \,\,x = 3\,km\]
It’s a required solution.

So, the correct answer is “Option B”.

Note: The boat and stream concept is one of the most common topics based on which questions are asked in the various Government exams in the quantitative aptitude section.
The four terms which are important for a candidate to know to understand the concept of streams are:
Stream – The moving water in a river is called a stream.
Upstream – If the boat is flowing in the opposite direction to the stream, it is called upstream. In this case, the net speed of the boat is called the upstream speed
Downstream – If the boat is flowing along the direction of the stream, it is called downstream. In this case, the net speed of the boat is called downstream speed
Still Water – Under this circumstance the water is considered to be stationary and the speed of the water is zero.