Question

A man crosses a 320 m wide river perpendicular to the current in 4 mm. If in still water he can swim with a speed 5/3 times that of the current, then the speed of the current, in m/min is

• A. $30$
• B. $40$
• C. $50$
• D. $60$

Answer 1

The correct option is D

$60$

Explanation for correct option:

Option (D): $60$

Given, Width of the river (d) = 320 m

Speed of the current = u

Speed of the man (v) = $\frac{5}{3}u$

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

$\Rightarrow 4=\frac{320}{\sqrt{{\displaystyle \frac{5}{3}}{u}^2-u^2}}$

$\Rightarrow 4=\frac{320}{{\displaystyle \frac{4}{3}}u}$

$\Rightarrow u=60meter/minute$

Therefore, the speed of the current is 60 meters/minute.

Hence, Option (D) is the correct answer.