Quantitative Aptitude

Pipes and Cisterns

535 Questions
All Delayed opening or closing 106 Combined pipes and the LCM shortcut 77 Find unknown pipe time 64 Efficiency ratios and faster-pipe relations 61 Flow rates based on pipe diameter 50 Leaks and reverse-rate questions 50 Actual capacity and pump-rate equations 44 Partial filling or emptying condition 44 Alternating pipes and changing phases 39

Pipes and Cisterns Questions

Multiple choice

Two taps A and B can fill a cistern in 371/2 minutes and 45 minutes, respectively. Both taps are turned on. When must the second tap be turned off, so that the cistern is filled in half an hour?

  1. After 7 minutes

  2. After 9 minutes

  3. After 12 minutes

  4. After 5 minutes

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Tap A rate = 1 / 37.5 = 2/75. Tap B rate = 1/45. Let B be open for x minutes. (2/75 + 1/45)x + (2/75)(30-x) = 1. (6/225 + 5/225)x + 2/75(30-x) = 1. (11/225)*x + 0.8 - (2/75)x = 1. (11/225 - 6/225)x = 0.2. (5/225)x = 0.2. x/45 = 0.2. x = 9.

Multiple choice

A trapezium shaped tank is filled with a pipe with water flowing at the rate of 3.6 km/hr. The length of the tank is 1.25 m and the top and bottom are 20 m and 10 m, respectively. How much water can be filled in the tank in 20 minutes?

  1. 13000 m3

  2. 12250 m3

  3. 22500 m3

  4. 11000 m3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Flow rate = 3.6 km/hr = 1 m/s. In 20 minutes (1200 seconds), water length = 1200 m. Area of trapezium cross-section = (20 + 10) / 2 * 1.25 = 15 * 1.25 = 18.75 m^2. Volume = Area * length = 18.75 * 1200 = 22500 m^3.

Multiple choice

Two pipes A and B can fill a tank in 60 minutes and 75 minutes, respectively. There is also an outlet C. If A, B and C are opened together, the tank is full in 50 minutes. How much time will be taken by C to empty the full tank?

  1. 100 minutes

  2. 110 minutes

  3. 120 minutes

  4. 125 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rate of A = 1/60, Rate of B = 1/75. Combined rate (A+B) = 1/60 + 1/75 = (5+4)/300 = 9/300 = 3/100. Let C's rate be x. (A+B-C) = 1/50. So 3/100 - x = 1/50, which means x = 3/100 - 2/100 = 1/100. C takes 100 minutes.

Multiple choice

Two pipes A and B can fill a tank in 36 minutes and 45 minutes, respectively. Another pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. Total time taken for the tank to be filled up is

  1. 49 minutes

  2. 46 minutes

  3. 45 minutes

  4. 39 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A fills 1/36 per min, B fills 1/45 per min, C empties 1/30 per min. A+B fill (1/36 + 1/45) = 9/180 = 1/20 per min. In 7 mins, they fill 7/20. Remaining = 13/20. Then A+B-C = 1/36 + 1/45 - 1/30 = (5+4-6)/180 = 3/180 = 1/60. Time for remaining = (13/20) / (1/60) = 39 mins. Total = 7 + 39 = 46 mins.

Multiple choice

Directions: The following question is accompanied by statements (I), (II) and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the question. There are two types of pipes, type A and type B. In how many hours can one pipe of type A empty a tank? I. The pipe of type A is 2.5 times broader than the pipe of type B. II. Three pipes of type A and five pipes of type B can empty the tank in 4 hours. III. Six pipes of type A can empty the tank in the same time as 15 pipes of type B can do.

  1. Statements I and II

  2. Statements I and III

  3. Statement II and either I or III

  4. Any two statements

  5. All three statements
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement II provides a rate equation involving both pipe types. Statement I gives the ratio of their breadths (which relates to their flow rates), and Statement III gives the ratio of their efficiencies directly. Combining II with either I or III allows solving for the individual rates.

Multiple choice

Two pipes A and B can fill a tank in 15 hours and 20 hours, respectively. The third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. In how much time will the tank be full?

  1. 2 hours

  2. 3 hours 30 minutes

  3. 2 hours 30 minutes

  4. 1 hour

  5. 3 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rates: A=1/15, B=1/20, C=-1/25. Combined rate = 1/15 + 1/20 - 1/25 = (20+15-12)/300 = 23/300. In 10 hours, work done = 230/300 = 23/30. Remaining = 7/30. After C closes, rate = 1/15 + 1/20 = 7/60. Time = (7/30) / (7/60) = 2 hours.

Multiple choice

Two pipes can fill a cistern in 12 hours and 15 hours. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 20 minutes extra are taken for the cistern to be filled up. When the cistern is full, in what time will the leak empty it?

  1. 120 hours

  2. 130 hours

  3. 140 hours

  4. 160 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rate of pipes: 1/12 + 1/15 = 9/60 = 3/20. Time to fill = 20/3 hours = 6 hours 40 minutes. With leak, time taken = 6 hours 40 mins + 20 mins = 7 hours. Combined rate with leak = 1/7. Leak rate = 3/20 - 1/7 = (21-20)/140 = 1/140. Thus, the leak empties the cistern in 140 hours.

Multiple choice

A water tank is two-fifth full. Pipe A can fill the tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are opened, how long will it take to empty or fill the tank completely?

  1. 6 minutes to empty

  2. 9 minutes to fill

  3. 9 minutes to empty

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Tank is 2/5 full. Pipe A fills at 1/10 per min, Pipe B empties at 1/6 per min. Net rate = 1/10 - 1/6 = (3-5)/30 = -2/30 = -1/15 per min. To empty 2/5 of the tank: (2/5) / (1/15) = (2/5) * 15 = 6 minutes.

Multiple choice

Two pipes can fill a tank in 20 minutes and 24 minutes, respectively. A waste pipe can empty it at the rate of 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is

  1. 60 gallons

  2. 120 gallons

  3. 180 gallons

  4. 240 gallons
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the capacity be C. Rates are C/20, C/24, and -3. Together, C/20 + C/24 - 3 = C/15. Multiplying by 120: 6C + 5C - 360 = 8C, so 3C = 360, C = 120.

Multiple choice

A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water in the tank at the rate of 6 litres per minute. When the tank is full, the inlet pipe is opened and due to the leak, the tank is emptied in 12 hours. How many litres can the cistern hold?

  1. 7960

  2. 7840

  3. 8640

  4. 8290
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let capacity be C. Leak empties at rate C/8. Inlet fills at 6 L/min. Combined rate: (C/8 - 6*60) = C/12. C/8 - C/12 = 360. (3C - 2C)/24 = 360. C = 360 * 24 = 8640.