Question

A man can row at $5$ kph in still water. If the velocity of current is $1$ kph and it takes him $1$ hour to row to a place and come back, how far is the place?

• A. $2.4km$
• B. $2.5km$
• C. $3km$
• D. $3.6km$

Answer 1

The correct option is A

$2.4km$

Explanation for the correct option:

Speed of man in the water $=5kph$

Let $xkm$ be the required distance.

Downstream speed $=(speedofmaninwater+velocityofcurrent)$

$$\begin{gathered} =(5+1)km/hr \\ =6km/hr \end{gathered}$$

Time taken to cover $xkm$ at speed of $6km/hr=\frac{\text{Distance}}{\text{Speed}}=\frac{x}{6}hr$
and, Upstream speed $=(speedofmaninwater-velocityofcurrent)$

$$\begin{gathered} =(5-1)km/hr \\ =4km/hr \end{gathered}$$

Time taken to cover $xkm$ at speed of $4km/hr=\frac{\text{Distance}}{\text{Speed}}=\frac{x}{4}hr$
Since the total time taken is $1\text{hour}$

Therefore,
$$\begin{gathered} \left(\frac{x}{6}\right)+\left(\frac{x}{4}\right)=1 \\ \Rightarrow \frac{(2x+3x)}{12}=1 \\ \Rightarrow 5x=12 \\ \Rightarrow x=\frac{12}{5} \\ \Rightarrow x=2.4km \end{gathered}$$

Therefore, the required distance is $\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{}\mathit{k}\mathit{m}$.

Hence, the correct option is (A).