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A boat has a velocity relative to the still water that is twice the velocity of the stream in a river. If the boat crosses the river by the shortest path, the time taken is t₁ and when the same boat crosses the same river in the shortest time, the time taken is t₂. The ratio of t₁ : t₂is

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$2 : \sqrt{3}$

$\sqrt{3} : 2$

$\sqrt{5} : \sqrt{3}$

$\sqrt{3} : \sqrt{5}$

answer is A.

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Detailed Solution

$V_{B} = 2 V_{w}$
$t_{1} = \frac{b}{\sqrt{V_{B}^{2} - V_{W}^{2}}} = \frac{b}{\sqrt{3} . V_{w}}$
$t_{2} = \frac{b}{V_{B}} = \frac{b}{2 V_{w}}$
$\frac{t_{1}}{t_{2}} = \frac{2}{\sqrt{3}}$

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