Pipe A can independently empty a half-filled tank in 3 hours whereas pipe B can alone fill the same tank in 4 hours, when the tank is completely empty. In how much time will the empty tank be completely filled, if both the pipes are opened together ?
Answer & explanation
Correct answer: option 4
Pipe A empties a half-filled tank in $3$ hours
Half tank emptied in $3$ hours
Emptying rate of A
$=\frac{1/2}{3}=\frac{1}{6}$ tank per hour (emptying)
Pipe B fills the tank in $4$ hours
Filling rate of B
$=\frac{1}{4}$ tank per hour
Net rate when both are open
$=\frac{1}{4}-\frac{1}{6}$
$=\frac{3-2}{12}=\frac{1}{12}$ tank per hour
Time required to fill $1$ tank
$=\frac{1}{1/12}=12$ hours
The empty tank will be filled in $12$ hours.