A man crosses the river perpendicular to river flow in time t seconds and travels an equal distance down the stream in T seconds. The ratio of man’s speed in still water to the speed of river water will be:

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$\frac{T^{2} + t^{2}}{T^{2} - t^{2}}$

$\frac{T^{2} - t^{2}}{T^{2} + t^{2}}$

$\frac{t^{2} - T^{2}}{t^{2} + T^{2}}$

$\frac{t^{2} + T^{2}}{t^{2} - T^{2}}$

answer is C.

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Detailed Solution

$t = \frac{d}{\sqrt{u^{2} - v^{2}}}$

$d = (v + u) T$

From these equations

$\frac{v}{u} = \frac{t^{2} + T^{2}}{t^{2} - T^{2}}$

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