Tap A can fill a tank in 6 hours and another tap B can empty that full tank of water in 4 hours. If tap A is opened at 6 AM and after 3 hours tap B is opened, then the time by which the tank will be empty is

As per the question,

A can fill the tank in 6 hour.

So, A can fill the tank in one hour $$= \dfrac{1}{6}$$

Tap is open for 3 hour, so tank filled in 3 hour $$= \dfrac{3}{6}=\dfrac{1}{2}$$

Tap B can  empty the tank in 4 hour. So, tap B can empty the tank in one hour $$=\dfrac{1}{4}$$

Hence, tank will be empty in one hour $$=\dfrac{1}{4}-\dfrac{1}{6}=\dfrac{3-2}{12}=\dfrac{1}{12}$$

Hence, it will empty in 12 hour. Hence it will empty in $$\dfrac{12}{2}=6 hour$$

Time by which tank will be empty is 3:00PM