Filling and emptying tanks with inlet and outlet pipes.
45 solved questions · 15 easy · 20 medium · 10 hard
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Pipe A can fill a tank in 6 hours and pipe B in 12 hours. If both are opened together, how long will they take to fill the empty tank?
Answer: C. 4 hours
Solution
A fills 1/6 per hour, B fills 1/12 per hour Together = 1/6 + 1/12 = 3/12 = 1/4 Time = 4 hours Answer: 4 hours
Shortcut: Two inlets: (6 x 12)/(6 + 12) = 72/18 = 4 hours.
A pipe can fill a tank in 8 hours. What part of the tank will it fill in 3 hours?
Answer: A. 3/8
Solution
Part filled in 1 hour = 1/8 In 3 hours = 3/8 Answer: 3/8
An inlet pipe fills a tank in 10 hours and an outlet pipe empties the full tank in 15 hours. If both are opened together on the empty tank, how long will it take to fill it?
Answer: D. 30 hours
Solution
Net rate = 1/10 - 1/15 = 3/30 - 2/30 = 1/30 Time = 30 hours Answer: 30 hours
Shortcut: (10 x 15)/(15 - 10) = 30.
A pipe fills water at 20 litres per minute. How long will it take to fill an empty tank of 600 litres?
Answer: B. 30 minutes
Solution
Time = capacity / rate = 600 / 20 = 30 minutes Answer: 30 minutes
Pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. How long will they take together?
Answer: C. 12 minutes
Solution
1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 Time = 12 minutes Answer: 12 minutes
A full tank is emptied by an outlet pipe in 9 hours. What part of the tank is emptied in 4 hours?
Answer: A. 4/9
Solution
Part emptied in 1 hour = 1/9 In 4 hours = 4/9 Answer: 4/9
Two pipes can fill a tank in 15 hours and 10 hours respectively. How long will they take if opened together?
Answer: D. 6 hours
Solution
1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6 Time = 6 hours Answer: 6 hours
Pipe A is twice as fast as pipe B. Together they fill a tank in 8 minutes. How long will A alone take?
Answer: B. 12 minutes
Solution
Let A take x minutes, B takes 2x minutes 1/x + 1/(2x) = 1/8 3/(2x) = 1/8, so x = 12 A alone takes 12 minutes Answer: 12 minutes
A tank of 1,200 litres is filled by a pipe at 15 litres per minute. A leak empties 5 litres per minute. How long will it take to fill the empty tank?
Answer: C. 120 minutes
Solution
Net filling rate = 15 - 5 = 10 litres per minute Time = 1,200 / 10 = 120 minutes Answer: 120 minutes
A pipe fills one-fourth of a tank in 5 minutes. How long will it take to fill the whole tank?
Answer: A. 20 minutes
Solution
1/4 of the tank takes 5 minutes Whole tank = 5 x 4 = 20 minutes Answer: 20 minutes
Three pipes can fill a tank in 10, 15 and 30 minutes respectively. How long will they take if all three are opened together?
Answer: D. 5 minutes
Solution
1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5 Time = 5 minutes Answer: 5 minutes
A pipe fills a tank in 4 hours and a leak at the bottom empties it in 12 hours. How long will the pipe take to fill the empty tank with the leak open?
Answer: B. 6 hours
Solution
Net rate = 1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6 Time = 6 hours Answer: 6 hours
Pipe A fills a tank in 5 hours and pipe B empties the full tank in 20 hours. If both are open, how long will it take to fill the empty tank?
Answer: C. 6 2/3 hours
Solution
Net rate = 1/5 - 1/20 = 4/20 - 1/20 = 3/20 Time = 20/3 = 6 2/3 hours Answer: 6 2/3 hours
A pipe fills a 90-litre tank in 30 minutes. At how many litres per minute does it flow?
Answer: A. 3 litres per minute
Solution
Rate = 90 / 30 = 3 litres per minute Answer: 3 litres per minute
A tank is half full. Pipe A can fill the whole tank in 6 hours and pipe B in 3 hours. How long will both together take to fill the rest?
Answer: D. 1 hours
Solution
Together = 1/6 + 1/3 = 1/2 per hour Remaining = 1/2 of the tank Time = (1/2) / (1/2) = 1 hour Answer: 1 hours
Pipes A and B can fill a tank in 10 hours and 15 hours, and pipe C can empty it in 30 hours. If all three are opened together, how long will the tank take to fill?
Answer: B. 7 1/2 hours
Solution
Net rate = 1/10 + 1/15 - 1/30 = 3/30 + 2/30 - 1/30 = 4/30 = 2/15 Time = 7 1/2 hours Answer: 7 1/2 hours
Pipes A and B fill a tank in 12 and 15 hours respectively, and pipe C empties it in 20 hours. If all three are opened together, in how many hours will the empty tank be full?
Answer: C. 10 hours
Solution
Take capacity = LCM(12, 15, 20) = 60 units A = 5 units/h, B = 4 units/h, C = -3 units/h Net = 6 units/h Time = 60 / 6 = 10 hours Answer: 10 hours
Pipe A can fill a tank in 20 minutes and pipe B in 30 minutes. They are opened alternately, one minute each, A first. In how many minutes will the tank be full?
Answer: A. 24 minutes
Solution
A = 1/20, B = 1/30 per minute In a 2-minute cycle: 1/20 + 1/30 = 1/12 12 cycles fill the tank: 12 x 2 = 24 minutes Answer: 24 minutes
Pipe A fills a tank in 12 minutes and pipe B in 6 minutes. A is opened alone for 4 minutes and then B is opened as well. In how many minutes from the start is the tank full?
Answer: D. 6 2/3 minutes
Solution
A in 4 minutes = 4/12 = 1/3 Remaining = 2/3 A + B = 1/12 + 1/6 = 1/4 per minute Time for the rest = (2/3) / (1/4) = 8/3 minutes Total = 4 + 8/3 = 6 2/3 minutes Answer: 6 2/3 minutes
A pipe fills a tank in 6 hours. Because of a leak it takes 8 hours. In how many hours will the leak alone empty the full tank?
Answer: B. 24 hours
Solution
Leak rate = 1/6 - 1/8 = 4/24 - 3/24 = 1/24 The leak empties the full tank in 24 hours Answer: 24 hours
Shortcut: Leak time = (6 x 8)/(8 - 6) = 24.
A tap fills a tank at 4 litres per minute while an outlet drains 3 litres per minute. If the tank holds 240 litres, how long will it take to fill when both are open?
Answer: C. 240 minutes
Solution
Net rate = 4 - 3 = 1 litre per minute Time = 240 / 1 = 240 minutes Answer: 240 minutes
Pipes A and B fill a tank in 6 hours and 12 hours, and pipe C empties a full tank in 8 hours. If all three are opened together on an empty tank, how long will it take to fill?
Answer: A. 8 hours
Solution
Capacity = LCM(6, 12, 8) = 24 units A = 4, B = 2, C = -3 units per hour Net = 3 units per hour Time = 24 / 3 = 8 hours Answer: 8 hours
Pipes A and B can fill a tank in 20 and 30 minutes. Both are opened together, but after 6 minutes B is closed. In how many minutes from the start will the tank be full?
Answer: D. 16 minutes
Solution
A + B = 1/20 + 1/30 = 1/12 per minute In 6 minutes = 1/2 Remaining 1/2 is filled by A alone: (1/2) x 20 = 10 minutes Total = 6 + 10 = 16 minutes Answer: 16 minutes
A tank is two-thirds full. An outlet pipe can empty a full tank in 12 hours. How long will it take to empty the tank?
Answer: B. 8 hours
Solution
Part to empty = 2/3 Time = (2/3) x 12 = 8 hours Answer: 8 hours
A tank is one-fourth full. A pipe can fill the whole tank in 12 hours. How long will it take to fill the rest?
Answer: C. 9 hours
Solution
Part left = 3/4 Time = (3/4) x 12 = 9 hours Answer: 9 hours
Pipes A and B can fill a tank in 36 and 45 minutes. Both are opened together, and B is closed after some time so that the tank is full in exactly 30 minutes. For how many minutes was B open?
Answer: A. 7 1/2 minutes
Solution
A works all 30 minutes: 30/36 = 5/6 of the tank B fills the remaining 1/6: time = (1/6) x 45 = 7.5 minutes B was open for 7 1/2 minutes Answer: 7 1/2 minutes
A pipe fills a 300-litre tank in 12 minutes. With a leak open it takes 15 minutes. How many litres per minute does the leak lose?
Answer: D. 5 litres per minute
Solution
Pipe rate = 300 / 12 = 25 litres per minute Net rate with leak = 300 / 15 = 20 litres per minute Leak = 25 - 20 = 5 litres per minute Answer: 5 litres per minute
Pipes A and B can fill a tank in 8 hours and 12 hours. With a third pipe C (an outlet) also open, the empty tank fills in 12 hours. How long will C alone take to empty the full tank?
Answer: B. 8 hours
Solution
A + B = 1/8 + 1/12 = 5/24 With C open: 1/12 = 2/24 C = 5/24 - 2/24 = 3/24 = 1/8 C empties the full tank in 8 hours Answer: 8 hours
Pipes A and B fill a tank in 20 minutes and 30 minutes, and pipe C empties a full tank in 15 minutes. If all are opened together, how long will it take to fill the empty tank?
Answer: C. 60 minutes
Solution
Capacity = 60 units: A = 3, B = 2, C = -4 units per minute Net = 1 unit per minute Time = 60 minutes Answer: 60 minutes
Two taps fill a tank at 9 and 6 litres per minute, while a waste pipe removes 5 litres per minute. How many minutes will an empty 1,500-litre tank take to fill with all three open?
Answer: A. 150 minutes
Solution
Net rate = 9 + 6 - 5 = 10 litres per minute Time = 1,500 / 10 = 150 minutes Answer: 150 minutes
Pipe A fills a tank in 6 hours and pipe B empties it in 8 hours. A is opened alone for the first 2 hours and then B is also opened. In how many hours from the start will the tank be full?
Answer: D. 18 hours
Solution
A in 2 hours = 2/6 = 1/3 Remaining = 2/3 Net with both = 1/6 - 1/8 = 1/24 Time for the rest = (2/3) x 24 = 16 hours Total = 2 + 16 = 18 hours Answer: 18 hours
Pipes A and B together fill a tank in 20 minutes. Pipe A alone takes 30 minutes. How long will B alone take?
Answer: B. 60 minutes
Solution
B = 1/20 - 1/30 = 3/60 - 2/60 = 1/60 B alone takes 60 minutes Answer: 60 minutes
A tank is half full. A pipe adds 1/6 of the tank every hour and an outlet removes 1/12 of the tank every hour. How long will it take to fill the rest with both open?
Answer: C. 6 hours
Solution
Net rate = 1/6 - 1/12 = 1/12 of the tank per hour Remaining = 1/2 Time = (1/2) / (1/12) = 6 hours Answer: 6 hours
Pipe A is three times as fast as pipe B. Together they fill a tank in 9 minutes. How long will B alone take?
Answer: A. 36 minutes
Solution
Let A take x minutes, B takes 3x 1/x + 1/(3x) = 4/(3x) = 1/9 x = 12, so B takes 3 x 12 = 36 minutes Answer: 36 minutes
A tank is one-third full. Pipes A and B can fill a full tank in 10 hours and 15 hours respectively. How long will both take together to fill the rest?
Answer: D. 4 hours
Solution
Together = 1/10 + 1/15 = 1/6 per hour Remaining = 2/3 Time = (2/3) x 6 = 4 hours Answer: 4 hours
Pipes A and B fill a tank in 12 and 18 hours, and pipe C empties it in 9 hours. A and B are opened first. After 4 hours C is also opened. In how many hours from the start will the tank be full?
Answer: B. 20 hours
Solution
A + B = 1/12 + 1/18 = 5/36 per hour; in 4 hours = 20/36 = 5/9 Remaining = 4/9 With C: 5/36 - 4/36 = 1/36 per hour Time for the rest = (4/9) x 36 = 16 hours Total = 4 + 16 = 20 hours Answer: 20 hours
Pipe A fills a tank in 4 hours, pipe B empties it in 6 hours and pipe C fills it in 12 hours. They are opened one at a time for one hour each in the order A, B, C, A, B, C, ... In how many hours will the empty tank be full?
Answer: C. 15 2/3 hours
Solution
In one hour: A = +1/4, B = -1/6, C = +1/12 In a 3-hour cycle: 3/12 - 2/12 + 1/12 = 2/12 = 1/6 After 5 cycles (15 hours) the tank is 5/6 full Hour 16 (pipe A): only 1/6 is needed and A fills 1/4 per hour, so it needs (1/6) / (1/4) = 2/3 hour Total = 15 2/3 hours Answer: 15 2/3 hours
Pipes A and B can fill a tank in 12 hours and 20 hours. When both are open together with a leak, the tank fills in 10 hours. How long will the leak alone take to empty the full tank?
Answer: A. 30 hours
Solution
A + B = 1/12 + 1/20 = 5/60 + 3/60 = 8/60 = 2/15 With the leak = 1/10 Leak = 2/15 - 1/10 = 4/30 - 3/30 = 1/30 The leak empties the tank in 30 hours Answer: 30 hours
Pipes A and B fill a tank in 12 minutes and 20 minutes. Both are opened, but A is closed after some time and B alone finishes the job so that the tank is full in 15 minutes in all. After how many minutes was A closed?
Answer: D. 3 minutes
Solution
B works all 15 minutes: 15/20 = 3/4 of the tank A fills the remaining 1/4: time = (1/4) x 12 = 3 minutes A was closed after 3 minutes Answer: 3 minutes
A tank of 1,050 litres is filled by two taps at 20 and 30 litres per minute while a drain removes 15 litres per minute. All three start open on the empty tank, but the drain is closed after 10 minutes. How many minutes in all does the tank take to fill?
Answer: B. 24 minutes
Solution
First 10 minutes: net = 20 + 30 - 15 = 35 litres per minute, so 350 litres Left = 1,050 - 350 = 700 litres After the drain is shut, rate = 50 litres per minute: 700 / 50 = 14 minutes Total = 10 + 14 = 24 minutes Answer: 24 minutes
Pipe A fills a tank 2 hours faster than pipe B. Together they fill it in 2 hours 24 minutes. How long will B alone take?
Answer: C. 6 hours
Solution
Together time = 2 h 24 min = 12/5 hours, so combined rate = 5/12 Let A take x hours, B takes (x + 2) 1/x + 1/(x + 2) = 5/12 12(2x + 2) = 5x(x + 2) 5x^2 - 14x - 24 = 0, so (5x + 6)(x - 4) = 0, x = 4 A = 4 hours, B = 6 hours Answer: 6 hours
A pipe can fill a tank in 4 hours. After the tank is half full, a leak develops, and the second half takes 4 more hours to fill. In how many hours would the leak alone empty the full tank?
Answer: A. 8 hours
Solution
Pipe fills 1/4 per hour With the leak, the second half (1/2) takes 4 hours, so net rate = 1/8 Leak rate = 1/4 - 1/8 = 1/8 The leak empties the full tank in 8 hours Answer: 8 hours
A tank of 2,400 litres is filled by taps at 30 and 20 litres per minute and drained at 25 litres per minute. The drain is closed after 20 minutes. How long does the tank take to fill in all?
Answer: D. 58 minutes
Solution
First 20 minutes: net = 30 + 20 - 25 = 25 litres per minute, so 500 litres Left = 1,900 litres at 50 litres per minute = 38 minutes Total = 20 + 38 = 58 minutes Answer: 58 minutes
Pipes A and B fill a tank in 6 hours and 8 hours. They are opened together for 2 hours, and then an outlet C is also opened. The tank then fills in 6 more hours. In how many hours can C alone empty the full tank?
Answer: B. 4 1/2 hours
Solution
A + B = 1/6 + 1/8 = 7/24 per hour; in 2 hours = 7/12 Remaining = 5/12, filled in 6 hours, so net rate = 5/72 C = 7/24 - 5/72 = 21/72 - 5/72 = 16/72 = 2/9 C empties the tank in 9/2 = 4 1/2 hours Answer: 4 1/2 hours
Pipe A can fill a tank in 12 minutes and pipe B can empty it in 18 minutes. They are opened alternately for one minute each, A first. In how many minutes will the empty tank be full?
Answer: C. 67 minutes
Solution
A = +1/12, B = -1/18 per minute In a 2-minute cycle: 1/12 - 1/18 = 3/36 - 2/36 = 1/36 After 33 cycles (66 minutes) the tank is 33/36 = 11/12 full The 67th minute is A's: it adds 1/12, which is exactly what is left Dividing by 1/36 per cycle would give 72 minutes, but the tank fills earlier, during an A minute Total = 67 minutes Answer: 67 minutes
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