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

During Holi, two taps can fill a tub in 15 minutes and 20 minutes, respectively. Both the taps are opened at the same time, but after 4 minutes, first tap pipe is closed. In how much time will the tub be filled fully?

  1. 14 minutes and 40 seconds

  2. 12 minutes and 30 seconds

  3. 11 minutes and 45 seconds

  4. 10 minutes and 30 seconds

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

Tap 1 fills 1/15 per min, Tap 2 fills 1/20 per min. In 4 mins, they fill 4 * (1/15 + 1/20) = 4 * (7/60) = 7/15. Remaining = 8/15. Tap 2 fills this in (8/15) / (1/20) = 160/15 = 10.66 mins (10 min 40 sec). Total time = 4 + 10 min 40 sec = 14 min 40 sec.

Multiple choice

A water tank has eight pipes fitted into it. Pipes are of two types: Green Pipe and Red Pipe. Green pipes are used to fill the tank and the Red pipes are used to empty the tank. Every Green pipe can fill the tank in 12 hours and every Red pipe can empty it in 36 hours. On opening all the pipes an empty tank is filled in 3 hours. The number of Red pipes is

  1. 5

  2. 3

  3. 4

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let G be the number of green pipes and R be the number of red pipes. G+R=8. The net rate is (G/12) - (R/36) = 1/3. Substituting R=8-G: (G/12) - ((8-G)/36) = 1/3. Multiplying by 36: 3G - 8 + G = 12, so 4G = 20, G=5. Thus R=3.

Multiple choice

Water is following at the rate of 5 km/hr. through a cylindrical pipe of diameter 14 cm. into a rectangular tank which is 50 m. long and 44 m wide. Find the time in which the level of water in the tank will rise by 7 cm.

  1. 1 hr.

  2. 2 hr.

  3. 3 hr.

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

Water flows through cylindrical pipe at 5 km/hr. Pipe diameter = 14 cm, so radius = 7 cm = 0.07 m. Volume of water flowing per hour = π × r² × length = π × (0.07)² × 5000 m³ (converting 5 km to 5000 m). This is π × 0.0049 × 5000 = 24.5π m³/hr. Tank dimensions: 50 m × 44 m, rise needed = 7 cm = 0.07 m. Volume needed = 50 × 44 × 0.07 = 154 m³. Time = Volume needed / Flow rate = 154 / (24.5π) hours. Using π ≈ 22/7: 24.5π = 24.5 × 22/7 = 77. So Time = 154 / 77 = 2 hours. The answer is 2 hours.

Multiple choice

Pipe A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than a to fill the cistern then the time in which A will fill the cistern separately will be -

  1. 15 minutes

  2. 20 minutes

  3. 10 minutes

  4. 25 minutes

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

Let A's time = t minutes. Then B's time = t + 5. Combined rate: 1/t + 1/(t+5) = 1/6. Solving: (t+5 + t) / t(t+5) = 1/6, giving 6(2t+5) = t(t+5). This leads to 12t + 30 = t² + 5t, or t² - 7t - 30 = 0. Factoring: (t-10)(t+3) = 0, so t = 10. Options A and B are too long. Option D is too long.

Multiple choice

(\text{Inlet Pipe A can fill the tank in one hour. Outlet pipe B can empty it in 3 hours. Both pipes working together may fill the tank at a rate of 8000 lit/hour. Find the capacity of the tank.})
  1. $12000 lit$
  2. $8000 lit$
  3. $6000 lit$
  4. $4000 lit$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Inlet A fills 1 tank/hour (rate +1 tank/hr), outlet B empties in 3 hours (rate -1/3 tank/hr). Combined rate = 1 - 1/3 = 2/3 tank/hr. If 2/3 tank = 8000 lit/hr, then full tank = 8000 ÷ (2/3) = 8000 × (3/2) = 12000 lit. Option B (8000 lit) is just the fill rate, not capacity. Option C (6000 lit) would mean combined rate is 4/3 tank/hr, impossible. Option D (4000 lit) gives combined rate 2 tank/hr, exceeding inlet's capacity.

Multiple choice

A pump can fill a cistern in 40 minutes and another pump can empty the filled up cistern in 1 hour. By mistake, without closing the second pump, the first pump is opened. The time in which the empty cistern will be filled up is-

  1. 3 hours

  2. 4 hours

  3. 1 hour

  4. 2 hours

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

First pump fills in 40 minutes, rate = 1/40 per minute. Second pump empties in 60 minutes, rate = -1/60 per minute. Net rate = 1/40 - 1/60 = (3-2)/120 = 1/120 per minute. Time to fill = 120 minutes = 2 hours. Option D matches.

Multiple choice

Two pipes A and B can fill a tank in 28 minutes and 42 minutes respectively. Another pipe can empty that tank in 42 minutes. If all three are opened simultaneously, in what time tank will be filled?

  1. 30 min.

  2. 35 min.

  3. 28 min.

  4. 42 min.

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

Pipe A fills at 1/28 tank per minute, pipe B fills at 1/42 tank per minute, and the emptying pipe removes at 1/42 tank per minute. Combined rate = 1/28 + 1/42 - 1/42 = 1/28 tank per minute. Therefore, the tank fills in 28 minutes. The emptying pipe cancels out pipe B's contribution exactly.

Multiple choice

One fill pipe ‘A’ is 3 times faster than second fill pipe ‘B’ and takes 32 minutes less than the fill pipe ‘B’. When will the cistern be full if both pipes are opened together?

  1. 8 minute

  2. 12 minute

  3. 6 minute

  4. 16 minute

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

Let B's time = x minutes. A is 3× faster, so A's time = x/3 minutes. Given x - x/3 = 32, so 2x/3 = 32, giving x = 48 minutes for B alone. A alone takes 48/3 = 16 minutes. Together: 1/16 + 1/48 = 3/48 + 1/48 = 4/48 = 1/12, so they fill the cistern in 12 minutes. Answer B is correct.

Multiple choice

A cistern is normally filled in 8 hours but takes 2 hours longer to fill because of a leak in its bottom. If the tap that is filling the tank is turned off, then how much time will it take the leak take to empty the tank, if it is completely filled.

  1. 14

  2. 28

  3. 16

  4. 22

  5. 40
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let the tank capacity be 1 unit. Normal fill rate = 1/8 per hour. With leak, fill rate = 1/10 per hour (takes 10 hours). The leak empties at rate = (1/8 - 1/10) = (5-4)/40 = 1/40 per hour. If the tap is turned off and tank is full, the leak alone would take 40 hours to empty it (1 / (1/40) = 40).

Multiple choice

Water flows into a tank 15 m.×10 m. through a rectangluar pipe 2 m. × 1.5 m. at 20 km./hr. In how much time will the water level in the tank rise by 3 m.?

  1. 15 seconds

  2. 19 seconds

  3. 23 seconds

  4. 27 seconds
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of water needed = tank area × height rise = 15 × 10 × 3 = 450 m³ = 450,000 L. Water flow per second = pipe area × velocity = (2 × 1.5) × (20 × 1000/3600) = 3 × (20000/3600) = 3 × 5.56 = 16.67 m³/s. Time = 450/16.67 = 27 seconds.

Multiple choice

Pipes P and Q can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all three are opened at 7 a.m. at what time will one-fourth of the tank be filled?

  1. 10 a.m.

  2. 10 p.m.

  3. 11 p.m.

  4. 11 a.m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Combined rate when all three pipes work: 1/10 + 1/12 - 1/6 = (6 + 5 - 10)/60 = 1/60 tank per hour (negative because C empties). To fill 1/4 tank: time = (1/4) / (1/60) = 15 hours. Starting at 7 a.m. + 15 hours = 10 p.m.