Single correct option
Pipe A can fill a tank in 10 hours and pipe B in 15 hours, while pipe C can empty the full tank in 12 hours. All three pipes are opened at 9 a.m. on an empty tank, and C is closed at 11 a.m. At what time will the tank be full?
- A. 3 p.m.
- B. 3:30 p.m.
- C. 4 p.m.
- D. 5 p.m.
Show answer and solution
Answer: (C) 4 p.m.
Net rate with all three open = 1/10 + 1/15 − 1/12 = (6 + 4 − 5)/60 = 5/60 = 1/12 per hour.
From 9 to 11 a.m. (2 hours): filled = 2/12 = 1/6.
After C is closed, the rate = 1/10 + 1/15 = 1/6 per hour. Remaining 5/6 takes (5/6)/(1/6) = 5 hours.
The tank is full 5 hours after 11 a.m., at 4 p.m.
Why not 3 p.m.? That comes from ignoring C's emptying during the first 2 hours.
From 9 to 11 a.m. (2 hours): filled = 2/12 = 1/6.
After C is closed, the rate = 1/10 + 1/15 = 1/6 per hour. Remaining 5/6 takes (5/6)/(1/6) = 5 hours.
The tank is full 5 hours after 11 a.m., at 4 p.m.
Why not 3 p.m.? That comes from ignoring C's emptying during the first 2 hours.
Saved on this device. Sign in or create a free account to keep it on every device.