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A boat can go across a lake and return in time T₀ at a speed V. On a rough day there is uniform current at speed u 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/T₀ =

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

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

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

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

answer is B.

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Detailed Solution

$T_{0} = \frac{d}{v}$

$T = \frac{d}{(v + u)} - \frac{d}{(v - u)} = \frac{2 d v}{v^{2} - u^{2}}$

Therefore

$\frac{T}{T_{0}} = \frac{1}{1 - \frac{u^{2}}{V^{2}}}$

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