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On a calm day a boat can go across a lake and return in time $T_{0}$ at a speed $V$ . On a rough day there is a 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

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$1 + v^{2} / V^{2}$

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

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

$1 - v^{2} / V^{2}$

answer is B.

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Detailed Solution

$T_{0} = \frac{2 s}{V}$
and $T = \frac{s}{V + v} + \frac{s}{V - v} = \frac{2 s V}{V^{2} - v^{2}}$
$∴ T / T_{0} = \frac{(2 s V / V^{2} - v^{2})}{2 s / V}$
$= \frac{V^{2}}{V^{2} - v^{2}} = \frac{1}{1 - v^{2} / V^{2}}$

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