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 pipes can fill a tank in 12 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to permanent leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If A and B opens for 5 hours then closed, in what time would the leak empty it?

  1. 75

  2. 72

  3. 78

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe A rate = 1/12 per hour, Pipe B rate = 1/20 per hour. Combined rate = 1/12 + 1/20 = 8/60 = 2/15 tank per hour, so they should fill in 7.5 hours normally. But with leak, they take 8 hours (30 min extra). Actual rate with leak = 1/8 per hour. Leak rate = 2/15 - 1/8 = 1/120 per hour (empties). After pipes fill for 5 hours: 5 × (2/15) = 2/3 tank filled. Leak empties at 1/120 per hour, so to empty 2/3 tank: (2/3)/(1/120) = 80 hours. Option D claims 80 but the leak would empty a FULL tank in 120 hours, not 75.

Multiple choice

Pipe A and Pipe B can fill a tank in 10 hours and 15 hours respectively. When a third pipe C which work as an outlet pipe is also open then the tank can be filled in 18 hours. The outlet pipe can empty a full tank in :

  1. 12

  2. 8

  3. 9

  4. 14

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

A fills in 10 hrs → rate = 1/10 tank/hr. B fills in 15 hrs → rate = 1/15 tank/hr. C empties in x hrs → rate = -1/x tank/hr. Combined rate when all open: 1/10 + 1/15 - 1/x = 1/18. Solving: (3+2)/30 - 1/x = 1/18 → 5/30 - 1/x = 1/18 → 1/6 - 1/18 = 1/x → (3-1)/18 = 1/x → 2/18 = 1/x → x = 9 hrs.

Multiple choice

Pipe A and B can fill a tank in one hour and two hour respectively while pipe C can empty the filled up tank in one hour and fifteen minute. A and C are turned on together at 9am after two hour, only A is closed and B is turned on. When will the tank be emptied?

  1. 12:10 pm

  2. 11:30 pm

  3. 10:30 pm

  4. 12:20 pm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A fills at 1 tank/hour, B fills at 0.5 tank/hour, and C empties at 0.8 tank/hour (since 1h15m = 5/4 hours). When A and C work together, net rate = 1 - 0.8 = 0.2 tank/hour. In 2 hours, they fill 0.4 tank. After 2 hours, A stops and B joins C, giving net rate = 0.5 - 0.8 = -0.3 tank/hour. To empty 0.4 tank at 0.3 tank/hour takes 4/3 hours = 1 hour 20 minutes. Starting from 9am + 2 hours + 1h20m = 12:20pm.

Multiple choice

A tap takes 42 hours extra to fill a tank due to leakage equivalent to half of its inflow. The inlet pipe alone can fill the tank in how many hours?

  1. 42

  2. 21

  3. 36

  4. 28

  5. 30
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the inlet pipe's rate be 1 unit per hour, so it fills the tank in x hours (tank capacity = x units). The leak drains at half the inflow rate = 0.5 units per hour. Net fill rate with leak = 1 - 0.5 = 0.5 units per hour. Time with leak = tank capacity / net rate = x / 0.5 = 2x hours. Given: 2x - x = 42 hours (the extra time due to leak). So x = 42 hours. The inlet pipe alone takes 42 hours. This matches option A.

Multiple choice

A cistern has two pipes connected with it. One can fill it in 8 hours and other can empty it in 5 hours. In how many hours will the cistern be emptied if both the pipes are opened together when 3/4 of the cistern is already full of water?

  1. 5

  2. 10

  3. 7

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The fill pipe fills at 1/8 cistern per hour, the empty pipe empties at 1/5 per hour. Combined rate = 1/8 - 1/5 = -3/40 per hour (emptying). To empty 3/4 of the cistern: Time = (3/4) / (3/40) = 10 hours. The negative sign indicates emptying.

Multiple choice

Pipe A can fill an empty tank in 30 hours while B can fill it in 45 hours. Pipe A and B are opened and closed alternatively i.e., first pipe A is opened, then B, again A and then B and so on for 1 hour each time without any time lapse. In how many hours the tank will filled if it was empty initially?

  1. 36

  2. 54

  3. 48

  4. 60

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

A fills 1/30 per hour, B fills 1/45 per hour. In 2 hours (A then B), tank fills by 1/30 + 1/45 = 5/90 = 1/18. After 36 hours (18 cycles), tank fills by 18/18 = 1. Each full cycle takes 2 hours. 36 hours ÷ 2 hours/cycle = 18 complete cycles.

Multiple choice

Two pipe A, B can fill a tank in 30 and 15 hours whereas a third pipe can empty it in 12 hours. If all the pipes are open alternatively starting by A and followed by B and C. Find in how many hours the tank will be filled?

  1. 167 hours

  2. 164 hours

  3. 180 hours

  4. 172 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A fills 1/30 per hour, B fills 1/15 per hour, C empties 1/12 per hour. Net fill per 3-hour cycle (A then B then C) = 1/30 + 1/15 - 1/12 = (2+4-5)/60 = 1/60. After 486 hours (162 cycles), tank is 486/60 = 8.1 full (overflow). Starting from empty: after 162 cycles = 483 hours, tank has 162/60 = 2.7. Hour 484 (A): 2.7 + 1/30 = 2.733. Hour 485 (B): 2.733 + 1/15 = 2.8. Hour 486 (C): 2.8 - 1/12 = 2.717. Need total of 1. After 164 hours (54 cycles + 2 hours): 54/60 + 1/30 + 1/15 = 0.9 + 0.033 + 0.067 = 1.0. So 164 hours (Option B).

Multiple choice

A bathtub can be filled by the cold water pipe in 20 minutes and by the hot water pipe in 30 minutes. A person leaves the bathroom after turning on both the pipes simultaneously and returns at the moment when the bath should be full. Finding, however, that the waste pipe has been open, he now closes it. In 6 minutes more the bathtub is full. In what time would the waste pipe empty it?

  1. 16

  2. 29

  3. 24

  4. 27

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

Let waste pipe empty in x minutes (rate = 1/x per minute). Cold fills at 1/20 per minute, hot at 1/30 per minute. Combined fill rate = 1/20 + 1/30 - 1/x = 5/60 - 1/x. The tub should be full in 1/(1/20+1/30) = 12 minutes with all three pipes working normally. But when waste is open, it takes 12 + 6 = 18 minutes to fill. In those 18 minutes, actual fill occurred at rate (1/20 + 1/30) for full time, minus waste effect for 12 minutes. Actually: (1/20 + 1/30) × 18 - (1/x) × 12 = 1 (full tub). So 3/60 × 18 - 12/x = 1, giving 9/10 - 12/x = 1, so -12/x = 1/10, x = -120. That's wrong. Let me reconsider: The person expected tub to be full in 12 min (1/20+1/30=5/60=1/12). But when he returns, waste pipe has been open the whole time. In those 12 minutes, some water drained. Then he closes waste and it takes 6 more minutes to fill. In first 12 min: (1/20+1/30-1/x) × 12 = some fraction filled. Then in next 6 min: (1/20+1/30) × 6 = 6/12 = 1/2 fills remaining half. So first 12 min filled 1/2: (5/60-1/x) × 12 = 1/2. So 1 - 12/x = 1/2, giving 12/x = 1/2, x = 24 minutes. ✓

Multiple choice

Pipe P alone can fill up a cistern in 15 hours. Pipe Q alone can fill the same cistern in 20 hours. The pipes are simultaneously opened and it is found that due to a leakage at the bottom of the cistern, it takes 60/91 hours extra for the cistern to be completely filled. Calculate the time taken by the leak to empty the completely filled up cistern if both the pipes are closed.

  1. 100 hours

  2. 110 hours

  3. 120 hours

  4. 140 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe P fills in 15 hours, so rate = 1/15 per hour. Pipe Q fills in 20 hours, so rate = 1/20 per hour. Combined rate of P+Q = 1/15 + 1/20 = 7/60 per hour. Normal time to fill = 60/7 hours. With leak, time = 60/7 + 60/91 = (60×13)/91 = 780/91 hours. Actual fill rate = 91/780 per hour. Leak rate = (7/60) - (91/780) = (91-91)/780 = 0. Wait, let me recalculate: Combined rate of P+Q = 7/60. With leak, effective rate = 1/(60/7 + 60/91) = 1/((60×13 + 60)/91) = 91/(60×14) = 91/840. Leak rate = 7/60 - 91/840 = 98/840 - 91/840 = 7/840 = 1/120. So leak empties full tank in 120 hours. Option C is correct.

Multiple choice

Two pipes A and B can fill a tank independently in 10 hours and 15 hours respectively, while pipe C can empty it in 30 hours. All pipes are kept open for 6 hours after which pipes B and C are closed. In what time now onwards would the tank get full?

  1. 6

  2. 5

  3. 3

  4. 2

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

Combined rate with all pipes: 1/10 + 1/15 - 1/30 = 4/30 = 2/15 tank per hour. In 6 hours, tank fills 6 × 2/15 = 4/5. Remaining 1/5 is filled by A alone at rate 1/10 per hour. Time = (1/5) ÷ (1/10) = 2 hours. Option D is correct.

Multiple choice

Pipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 8 hours. Pipe A , B and C can fill the tank in 12 hours, then which of the statement is true for the pipe C?

  1. It can fill the tank in 4 hours 40 minutes

  2. It can empty the tank in 4 hours 40 minutes

  3. It can empty the tank in 4 hours 48 minutes

  4. It can fill the tank in 4 hours 48 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/6, B's rate = 1/8. Combined A+B = 7/24. With A+B+C = 1/12, C's rate = 1/12 - 7/24 = -5/24 (negative means emptying). Time to empty = 24/5 = 4.8 hours = 4h 48m.

Multiple choice

There are three pipes A, B & C that can fill a tank in 30, 40 and 60 hours respectively. A is opened at 7:00 AM, B at 8:00 AM and C at 10 AM, at what time the tank will be filled.

  1. 9: 20 PM

  2. 10: 00 PM

  3. 9: 30 PM

  4. 12: 30 PM
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A fills at 1/30 per hour, B at 1/40 per hour, C at 1/60 per hour. By 10 AM, A worked 3 hours: 3/30 = 1/10, B worked 2 hours: 2/40 = 1/20. Total filled = 1/10 + 1/20 = 3/20. Remaining = 17/20. All three together fill at 1/30 + 1/40 + 1/60 = (4+3+2)/120 = 9/120 = 3/40 per hour. Time for remaining: (17/20)/(3/40) = 34/3 = 11.33 hours = 11h 20m. Tank fills at 10 AM + 11h 20m = 9:20 PM.

Multiple choice

Two pipes B and F can fill the tank in 10 hours and 15 hours, respectively. If both the pipes are opened along with an outlet pipe M, then the tank is filled in 30 hours. Help me to find out how much time will the outlet pipe take to empty the full tank.

  1. 3.5

  2. 4.5

  3. 5.5

  4. 7.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Combined rate of B and F: 1/10 + 1/15 = 1/6. With outlet M open, net rate = 1/30. Let M's rate = 1/x. Then 1/6 - 1/x = 1/30, giving 1/x = 1/6 - 1/30 = 4/30 = 2/15. So M alone takes 15/2 = 7.5 hours to empty the tank.