Pipes A and B can fill an empty tank in 9 hours and 18 hours respectively, and pipe C can empty the full tank in 12 hours. The tank is empty at 6 a.m., when pipes A and B are opened. Pipe C is opened at 8 a.m. and closed at 11 a.m.; pipes A and B stay open throughout. At what time will the tank be full?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1:30 p.m.
Take the capacity as the LCM of 9, 18 and 12, that is 36 units, and follow the tank period by period, using only the pipes open in each period.
Per hour: A fills \(\frac{36}{9}=4\) units, B fills \(\frac{36}{18}=2\) units, C empties \(\frac{36}{12}=3\) units
6 a.m. to 8 a.m. (A and B, 2 hours): \(2\times(4+2)=12\) units
8 a.m. to 11 a.m. (A, B and C, 3 hours): \(3\times(4+2-3)=9\) units, so the tank holds \(12+9=21\) units at 11 a.m.
After 11 a.m. (A and B): left \(=36-21=15\) units, taking \(\displaystyle \frac{15}{6}=2\frac{1}{2}\) hours
11 a.m. \(+\) 2 hours 30 minutes \(=\) 1:30 p.m.
The tank is full at 1:30 p.m.