A man wishes to cross a river perpendicularly. In still water he takes 4 minutes to cross the river, but in… · ABC26GN3833

Subject: General Aptitude · Chapter: Boats and Streams · Exam: M.A.T. 2004

A man wishes to cross a river perpendicularly. In still water he takes 4 minutes to cross the river, but in flowing river he takes 5 minutes. If the river is 100 metres wide, the velocity of the flowing water of the river is
(a)10 m/min
(b)15 m/min
(c)20 m/min
(d)30 m/min
Answer
Answer (as printed): B
Explanation
Velocity of the river $=\left(100 \sqrt{\frac{1}{4^{2}}-\frac{1}{5^{2}}}\right) \mathrm{m} / \mathrm{min}$ $$\begin{aligned} = & \left(100 \sqrt{\frac{1}{16}-\frac{1}{25}}\right) \mathrm{m} / \mathrm{min} \\ = & \left(100 \sqrt{\frac{9}{400}}\right) \mathrm{m} / \mathrm{min} \\ = & \left(100 \times \frac{3}{20}\right) \mathrm{m} / \mathrm{min} \\ = & 15 \mathrm{m} / \mathrm{min} \end{aligned}$$

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