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Two identical boats A and B start from a point in a river with speed V relative to water in mutually perpendicular paths, A along the river current and B perpendicular to river current. If they move equal distances from initial point and return back, then find ratio of time taken by the boats A and B in round trips. Velocity of river current is 0.8V.

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$\frac{10}{3}$

$\frac{9}{3}$

$\frac{5}{3}$

$\frac{4}{3}$

answer is C.

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Detailed Solution

$t_{A} = \frac{l}{v + u} + \frac{l}{v - u}, t_{B} = \frac{l}{\sqrt{v^{2} - u^{2}}} + \frac{l}{\sqrt{v^{2} - u^{2}}}$

$\frac{t_{A}}{t_{B}} = \frac{5}{3}$

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