$A$ man swimming downstream overtakes a float at a point $M$. After travelling a distance $D$,he turns back and passes the float at a distance of $D/2$ from the point $M$. The ratio of the speed of the swimmer with respect to still water $(v_s)$ to the speed of the river $(v_r)$ is:

Two trains,each of length $100 \, m$,are moving parallel towards each other at speeds of $72 \, km/h$ and $36 \, km/h$ respectively. In how much time will they cross each other (in $, s$)?

$A$ boat is moving with a velocity of $3\hat i + 4\hat j$ in a river,and the water is moving with a velocity of $-3\hat i - 4\hat j$ with respect to the ground. The relative velocity of the boat with respect to the water is:

Two cars $A$ and $B$ are moving with the same speed of $45\,km/h$ along the same direction. If a third car $C$ coming from the opposite direction with a speed of $36\,km/h$ meets the two cars in an interval of $5\,min$,the distance of separation between the two cars $A$ and $B$ should be.......$km$.

$A$ person climbs up a stalled escalator in $60\,s$. If standing on the same but escalator running with constant velocity,he takes $40\,s$. How much time is taken by the person to walk up the moving escalator?........$s$

$Assertion$ : The magnitude of velocity of two boats relative to the river is the same. Both boats start simultaneously from the same point on one bank and may reach the opposite bank simultaneously while moving along different paths.
$Reason$ : For boats to cross the river in the same time,the component of their velocity relative to the river in the direction normal to the flow should be the same.