Tap A can fill the tank completely in 6 hrs while tap B can empty it by 12 hrs. By mistake, the person forgot to close the tap B, As a result, both the taps, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap B. In how much time now onwards, would the tank be full?
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill $\dfrac{1}{6}$ of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty $\dfrac{1}{12}$ of the tank
i.e., In one hour, Tank A and B together can effectively fill $\left(\dfrac{1}{6}-\dfrac{1}{12}\right)=\dfrac{1}{12}$ of the tank
=> In 4 hours, Tank A and B can effectively fill $\dfrac{1}{12}\times4=\dfrac{1}{3}$ of the tank.
Time taken to fill the remaining $\left(1-\dfrac{1}{3}\right)=\dfrac{2}{3}$ of the tank $=\dfrac{\left(\dfrac{2}{3}\right)}{\left(\dfrac{1}{6}\right)}$ = 4 hours