Let V be the total volume, $S_{D}$ is the speed of draining and $S_{P}$ is the speed of pumping.

It takes

30 minutesto empty ahalf-full tankby draining it at a constant rate

Half full tank = V / 2

Speed of draining ( $S_{D}$ ) = (V/2) / 30

$S_{D}$ = **V / 60 **

What is the rate at which water has to be pumped in so that it gets fully filled in

10 minutes

we have to fill in 10 minutes.

So, water drained in 10 minutes = (V/60) * 10

= V/6

water remained in tank = (V/2 – V/6) = V/3

water we have to pump = V – V/3 = 2V/3

Speed of pumping water ( $S_{P}$ ) = (2V/3) / 10

$S_{P}$ =** V / 15**

So, you can clearly see-

$S_{P}$ = ** 4 *** $S_{D}$

**Answer – A**