Question

A motorboat covers a given distance in $6$ hour moving downstream on a river. It covers the same distance in $10$ hour moving upstream. The time it takes to cover the same distance in still water is

• A. $9$ hours
• B. $7.5$ hours
• C. $6.5$ hours
• D. $8$ hours

Answer 1

The correct option is B

$7.5$ hours

Explanation for the correct option:

Step 1. Let, $W$ be the velocity of water and $M$ be the velocity of the motorboat in still water.

Distance covered by the boat downstream is

$\begin{array}{rcl}6h& =& x\end{array}$

$\Rightarrow$$\begin{array}{rcl}x& =& (M+W)\times 6\end{array}$…..(i)

Same distance $x$ covered by the motorboat in moving upstream in$10$ hours

$x=(M-W)\times 10$ …..(ii)

Step 2. Equating (i) and (ii), we get

$\begin{array}{rcl}(M+W)\times 6& =& (M-W)\times 10\end{array}$

$\Rightarrow$ $\begin{array}{rcl}6M+6W& =& 10M-10W\end{array}$

$\Rightarrow$$\begin{array}{rcl}10M-6M& =& 10W+6W\end{array}$

$\Rightarrow$ $\begin{array}{rcl}4M& =& 16W\end{array}$

$\Rightarrow$ $\begin{array}{rcl}W& =& \frac{4M}{16}\end{array}$

$\Rightarrow$ $\begin{array}{rcl}W& =& \frac{M}{4}\end{array}$

$\begin{array}{rcl}\therefore x& =& (M+W)x6\\ & =& 7.5M\end{array}$

Now,

Step 3. Time taken by the motorboat to cover the same distance in still water is,

$\begin{array}{rcl}\mathit{t}& \mathbf{=}& \frac{\mathbf{}\mathbf{x}}{\mathbf{M}}\end{array}$

$\begin{array}{rcl}& =& \frac{7.5M}{M}\\ & =& 7.5\end{array}$

$\therefore$The time it takes to cover the same distance in still water is $\mathbf{7}\mathbf{.}\mathbf{5}$ hours.

Hence, Option ‘C’ is Correct.