A man wishes to cross a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift of 120 m. If he crosses the river taking shortest route, he takes 12.5 minutes. Find velocity of the boat with respect to water.

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20 m/min

10 m/min

8 m/min

12 m/min

answer is A.

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Detailed Solution

$10 = \frac{L}{v}$ -------(i)

12.5 = $\frac{L}{\sqrt{v^{2} - u^{2}}} = \frac{L}{v \sqrt{1 - \frac{u^{2}}{v^{2}}}} - - - - (ii)$

$\frac{4}{5} = \sqrt{1 - \frac{12^{2}}{v^{2}}}$

$\frac{16}{25} = 1 - \frac{12^{2}}{v^{2}} \Rightarrow \frac{12^{2}}{v^{2}} = 1 - \frac{16}{25} = \frac{9}{25}$

$\frac{12}{v} = \frac{3}{5} \Rightarrow v = \frac{12 \times 5}{3} = 20 m / \min$

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