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
The correct answer is Option (4) → 12 hours
Pipe A empties half the tank in 3 hours, so it empties the full tank in 6 hours. Work per hour, as a part of the tank:
\( \displaystyle \text{B fills } \frac{1}{4}, \quad \text{A empties } \frac{1}{6} \)
With both pipes open:
\( \displaystyle \frac{1}{4} - \frac{1}{6} = \frac{3 - 2}{12} = \frac{1}{12} \)
The tank gains \(\frac{1}{12}\) of its capacity each hour, so it is full in 12 hours.