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 $120m$. If he crosses the river taking shortest route, he takes $12.5$ minutes, find velocity of the boat with respect to water.

The correct option is B $20m/min$
Draw a labelled diagram.

Find velocity of the boat with respect to water.

Case 1: For minimum time.
The time is given as,

$t_1=\frac{d}{v}$

$10=\frac{d}{v}\dots \dots \left(i\right)$

The drift is given as,

$u\times t_1=120$

$u\times (10\times 60)=120$

$u=\frac{1}{5}m/s$

Case 2: For the shortest route.

Let the angle with the river flow is $A$. The time is given as,

$t_2=\frac{d}{v\sin A}$

$12.5=\frac{d}{\sqrt{v^2-u^2}}\dots \dots \left(ii\right)$

Divide equation $\left(ii\right)$ in $\left(i\right)$,

$\frac{10}{12.5}=\frac{d}{v\times \frac{d}{\sqrt{v^2-u^2}}}$

$\frac{4}{5}=\sqrt{1-\frac{\frac{1}{25}}{v^2}}$

$v=\frac{1}{3}m/s$

$v=20m/min$