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A boat can go across a lake and return in time $t_{0}$ at a speed V. On a rough day, there is uniform current at speed v to help the onward journey and impede the return journey. If the time taken to go across and return on the rough day be t, then $t / t_{0}$ is equal to

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$1 - \frac{V^{2}}{V^{2}}$

$\frac{1}{1 - (v^{2} / V^{2})}$

$1 + \frac{v^{2}}{V^{2}}$

$\frac{1}{1 + (v^{2} / V^{2})}$

answer is B.

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Detailed Solution

Let l be the width of the lake. Then
$\begin{array}{l} t_{0} = \frac{2 l}{V} and t = \frac{l}{(V + v)} - \frac{l}{(V - v)} = \frac{2 lv}{V^{2} - v^{2}} \end{array}$

$\frac{t}{t_{0}} = \frac{1}{1 - (v^{2} / V^{2})}$

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