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

Pipes A and B can empty a fully filled tank in 8 and 12 hours respectively. C is a filling pipe. These three pipes were opened at the same time and in one hour the sixth part of the tank became empty in one hour. In how much time can C fill the tank alone? पाइप A और B एक पूरी तरह से भरे हुए टैंक को क्रमशः 8 और 12 घंटे में खाली कर सकते हैं। C एक भरने वाला पाइप है। इन तीनों पाइपों को एक साथ खोल दिया गया और एक घंटे में टंकी का छठा हिस्सा एक घंटे में खाली हो गया। C अकेले टंकी को कितने समय में भर सकता है?

  1. 25 hours 25 घंटे

  2. 20 hours 20 घंटे

  3. 30 hours 30 घंटे

  4. 24 hours 24 घंटे

  5. 22 hours 22 घंटे
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A and B are emptying pipes with rates 1/8 and 1/12 per hour. C is a filling pipe with unknown rate r. Together: 1/8 + 1/12 - r = 1/6 (emptying rate per hour). Solving: (3+2)/24 - r = 1/6, so 5/24 - r = 4/24, giving r = 1/24 per hour. Therefore C alone fills the tank in 24 hours. Option A (25 hours) would result if the net effect was slightly less than 1/6. Option C (30 hours) would require r = 1/30.

Multiple choice

Two pipes A and B fill a tank in 4 hours and 5 hours respectively. Both the pipes were filling the tank when after 60 minutes pipe A had some problem and was closed. How much time did it took to fill the tank completely?

  1. 2 hours 50 minutes

  2. 4 hours

  3. 3 hours 45 minutes

  4. 3 hours 30 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe A fills at 1/4 tank per hour, B at 1/5 tank per hour. Together they fill at (1/4 + 1/5) = 9/20 per hour. In 1 hour, they fill 9/20 of tank. Remaining = 11/20. Pipe B alone fills at 1/5 per hour, so time needed = (11/20) / (1/5) = 11/4 = 2.75 hours. Total time = 1 + 2.75 = 3.75 hours = 3 hours 45 minutes.

Multiple choice

A and B fill a tank in 12 minutes and 16 minutes respectively and pipe C can fill it in 8 minutes. A and B start filling the tank and after 5 minutes C starts filling the tank. In how much time will the tank be filled?

  1. 5 minutes

  2. 4 minutes

  3. 6 minutes

  4. 8 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combined rate of A and B = 1/12 + 1/16 = 7/48 per minute. In 5 minutes, they fill 5 × 7/48 = 35/48. Remaining = 13/48. With C added, combined rate = 1/12 + 1/16 + 1/8 = 13/48 per minute. Time for remaining = (13/48) / (13/48) = 1 minute. Total time = 6 minutes.

Multiple choice

Three pipes can fill a tank in 3 hours, 4 hours and 6 hours. However, there is a leak in the tank at a height of 1/3 of the tank from the bottom which can drain the rest of the tank in 9 hours. What will be the time taken to fill the tank?

  1. 94.45 minutes

  2. 89.28 minutes

  3. 75 minutes

  4. 84.5 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The three filling pipes together fill at rate 1/3 + 1/4 + 1/6 = 4/12 + 3/12 + 2/12 = 9/12 = 3/4 tank per hour. The leak affects only the top 2/3 of the tank. For the first 1/3, only filling pipes work: time = (1/3) / (3/4) = 4/9 hours. For the remaining 2/3, effective rate = 3/4 - 1/9 = (27-4)/36 = 23/36 tank per hour. Time = (2/3) / (23/36) = 24/23 hours. Total = 4/9 + 24/23 = (92+216)/207 = 308/207 hours = 1.488 hours = 89.28 minutes.

Multiple choice

A cistern is filled by 3 pipes A, B and C with uniform flow. The second pipe B takes (\frac{3}{2}) times the time taken by A to fill the tank, while C takes twice the time taken by B to fill the tank. If all the three pipes can fill the tank in 7 hours, find the time required by pipe A alone to fill the tank.

  1. 12

  2. 13

  3. 14

  4. 15

  5. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A take x hours. Then B takes (3/2)x hours and C takes 2 × (3/2)x = 3x hours. Combined rate: 1/x + 2/(3x) + 1/(3x) = 1/7. This simplifies to (3+2+1)/(3x) = 1/7, so 6/(3x) = 1/7, giving 2/x = 1/7, therefore x = 14 hours for pipe A alone.

Multiple choice

There are total 12 pipes to fill a reservoir in which some are fill pipes where as some are empty pipes. A fill pipe takes 30 minutes to fill reservoir completely, which is 60 minutes less than the time taken by an empty pipe to empty the reservoir. All working together takes 4.5 hr to completely fill the reservoir. If now one empty pipe starts working as fill pipe, what will be the time taken to fill the reservoir completely?

  1. 4.8 hr.

  2. 3 hr.

  3. 3.5 hr.

  4. 3.25 hr.

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

Fill pipe rate = 1/30 reservoir per minute. Empty pipe rate = 1/90 reservoir per minute. Let f = fill pipes, (12-f) = drain pipes. Combined rate = f/30 - (12-f)/90 reservoirs per minute = (3f - 12 + f)/90 = (4f - 12)/90. Time = 4.5 hours = 270 minutes. So 270 × (4f - 12)/90 = 1 → 3(4f - 12) = 1 → 12f - 36 = 1 → 12f = 37 → f = 37/12 ≈ 3.08. This isn't an integer - there's an inconsistency. If one drain becomes fill, new configuration still doesn't match given options. The calculated time (with corrected values) differs from all options A-D, so E is correct.

Multiple choice

Three pipes A, B and C can fill a tank in 12 hours, 20 hours and 30 hours respectively. All the three pipes are opened together, after some hours pipe A is closed. After another 3 hours, pipe B is closed and pipe C fills the remaining tank in 15 hours. What was the total time taken to fill the tank?

  1. 19.5 hours

  2. 18.5 hours

  3. 17.5 hours

  4. 16 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C work together for x hours. Work done in x hours: x(1/12 + 1/20 + 1/30) = x(20/240). Then A closes, B and C work for 3 hours: 3(1/20 + 1/30) = 3(5/60) = 1/4. Remaining work by C in 15 hours: 15/30 = 1/2. Total work = x/12 + 1/4 + 1/2 = 1. Solving: x/12 = 1/4, so x = 3 hours. Total time = 3 + 3 + 15 = 19.5 hours. Check: 3(20/240) + 1/4 + 1/2 = 1.

Multiple choice

Pipes P and Q can fill a tank in 18 and 27 minutes, respectively, whereas pipe R can empty the full tank in 54 minutes. P and Q were opened together for 6 minutes and then closed and R was opened. The tank was emptied by R alone in:

  1. 30 minutes

  2. 40 minutes

  3. 35 minutes

  4. 45 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P fills 1/18 per minute, Q fills 1/27 per minute. Together in 6 minutes: 6*(1/18+1/27) = 6*(5/54) = 30/54 = 5/9 tank filled. Remaining tank to empty = 5/9. R empties 1/54 per minute. Time = (5/9)/(1/54) = (5/9)*54 = 30 minutes.

Multiple choice

A rectangular water-tank measuring $\displaystyle 80\ cm\times 60\ cm\times 60\ cm$ is filled from a pipe of cross-sectional area 1.5 $\displaystyle cm^{2},$ the water emerging at 3.2 m/s. How long does it take to fill the tank?

  1. 10 minutes

  2. 15 minutes

  3. 13 minutes

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

Tank volume = 80 * 60 * 60 = 288000 cm^3. Pipe flow rate = Area * velocity = 1.5 cm^2 * 320 cm/s = 480 cm^3/s. Time = 288000 / 480 = 600 seconds = 10 minutes.

Multiple choice

A tank has 3 pipes. The first pipe can fill $\displaystyle\frac { 1 }{ 2 }$ part of the tank in 1 hour and the second pipe can fill $\displaystyle\frac { 1 }{ 3 }$ part in 1 hour. The third pipe is for making the tank empty. When all the three pipes are open, $\displaystyle\frac { 7 }{ 12 }$ part of the tank is filled in 1 hour. How much time will the third pipe take to empty the completely filled tank?
  1. $3$ hours
  2. $4$ hours
  3. $5$ hours
  4. $6$ hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The first pipe fills 1/2 per hour, the second 1/3 per hour. Together they fill 1/2 + 1/3 = 5/6 per hour. With the third pipe (C) open, the net rate is 7/12. Thus, 5/6 - C = 7/12. Solving for C gives 10/12 - 7/12 = 3/12 = 1/4. The third pipe empties 1/4 of the tank per hour, so it takes 4 hours to empty the full tank.

Multiple choice

A rectangular sump has an inner length and breadth of 24 m and 20 m respectively. Water flows through an inlet pipe at 180 m per minute. The cross-sectional area of the pipe is 0.5 m$^{2}$. The tank takes half an hour to get filled. Find the depth of the sump (in m).

  1. 4.625

  2. 6.125

  3. 5.625

  4. 5.125
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of water = Area * Velocity * Time = 0.5 * 180 * 30 = 2700 m^3. Volume of sump = Length * Breadth * Depth = 24 * 20 * Depth = 480 * Depth. 480 * Depth = 2700, so Depth = 2700 / 480 = 5.625 m.

Multiple choice

The surface of water in a swimming pool, when it is full of water, is rectangular with length and breadth $36\ m$ and $10.5\ m$ respectively. The depth of water increases uniformly from $1\ m$ at one end to $1.75\ m$ at the other end. The water in the pool is emptied by a cylindrical pipe of radius $7\ cm$ at the rate of $5\ km/h$. The time (in hours) to empty water in the pool is (take $\pi = \dfrac {22}{7})$.
  1. $6\dfrac {1}{4}$
  2. $6\dfrac {1}{2}$
  3. $6\dfrac {3}{4}$
  4. $6\dfrac {4}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of pool = Area * Average depth = (36 * 10.5) * ((1 + 1.75)/2) = 378 * 1.375 = 519.75 m^3. Pipe radius = 0.07m, speed = 5000m/h. Flow rate = Area * speed = pi * r^2 * v = (22/7) * 0.07^2 * 5000 = 77 m^3/h. Time = 519.75 / 77 = 6.75 hours = 6 3/4 hours.