Pipes A and B can fill an empty tank in 12 hours and 20 hours respectively, and pipe C can empty the full tank in 15 hours. The tank is empty at 8 a.m., when pipes A and B are opened. Pipe C is opened at 10 a.m. and closed at 1 p.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) → 5 p.m.
Take the capacity as the LCM of 12, 20 and 15, that is 60 units, and follow the tank period by period, using only the pipes open in each period.
Per hour: A fills \(\frac{60}{12}=5\) units, B fills \(\frac{60}{20}=3\) units, C empties \(\frac{60}{15}=4\) units
8 a.m. to 10 a.m. (A and B, 2 hours): \(2\times(5+3)=16\) units
10 a.m. to 1 p.m. (A, B and C, 3 hours): \(3\times(5+3-4)=12\) units, so the tank holds \(16+12=28\) units at 1 p.m.
After 1 p.m. (A and B): left \(=60-28=32\) units, taking \(\displaystyle \frac{32}{8}=4\) hours
1 p.m. \(+\) 4 hours \(=\) 5 p.m.
The tank is full at 5 p.m.