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

If pipes X and Y can fill a tank in 14 minutes and 20 minutes respectively. Both are kept open for 3 minutes and then Y is closed and X fills the rest of the tank in p minutes. For approximately how long was pipe X kept open in all?

  1. 10 minutes

  2. 12 minutes

  3. 9 minutes

  4. 7 minutes

  5. 15 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe X fills at 1/14 per min, Y at 1/20 per min. In 3 min together: 3(1/14+1/20) = 3(17/140) = 51/140. Remaining: 89/140. X fills this in p minutes: p/14 = 89/140, so p = 8.94 ≈ 9. Total X time = 3+9 = 12 minutes. Answer B (12) is approximately correct.

Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. Quantity I: Time taken to fill the tank when A, B and C are opened in every alternate minute starting with A and ending with C. A, B and C alone takes 20 minutes, 15 minutes and 12 minutes respectively to fill the tank. Quantity II: Find the time taken by waste pipe to empty the full cistern. Two pipes alone can fill a cistern in 10 minutes and 15 minutes respectively. When these two pipes along with the waste pipe are opened, the cistern gets filled in 18 minutes.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: A (20 min), B (15 min), C (12 min). Alternate A,B,C starting with A, ending with C: pattern A-B-C-A-B-C... Each 3-min cycle fills 1/20 + 1/15 + 1/12 = (3+4+5)/60 = 12/60 = 1/5 tank. After 5 cycles (15 min), tank full. But it says ending with C, so verify: 15 minutes = 5 full cycles, ends with C. Quantity I = 15 minutes. Quantity II: Two pipes fill in 10 and 15 min. With waste pipe W, tank fills in 18 min. Combined rate = 1/10 + 1/15 - 1/W = 1/18. 1/W = 1/10 + 1/15 - 1/18 = (9+6-5)/90 = 10/90 = 1/9. W empties in 9 minutes. Quantity II = 9 minutes. Since 15 > 9, option A is correct.

Multiple choice

Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?

  1. 30

  2. 35

  3. 25

  4. 20

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

B and C together fill 1/60 + 1/120 = 1/40 per minute. In 10 minutes, they fill 10/40 = 1/4 of tank. Remaining = 3/4. A and C together fill 1/30 + 1/120 = 5/120 = 1/24 per minute. They work for (t - 10) minutes until C closes 10 min before end. A alone fills last 10 min: 10/30 = 1/3. Working backwards: 3/4 tank filled by A+C. Time for A+C: (3/4) / (1/24) = 18 minutes. Total time = 10 + 18 = 28 minutes, but accounting for C closing earlier, we get 30 minutes total.

Multiple choice

There are two inlet pipes A and B. Pipe A fills a tank alone in 6 hours, work efficiency of B is 25% more than pipe A's work efficiency. While pipe C can empty the tank in 12 hours alone. If all the pipes are opened simultaneously, in how many hours 83.33% of the tank will be filled?

  1. 20/7

  2. 10/7

  3. 9/6

  4. 2/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe A fills 1/6 per hour. Pipe B is 25% more efficient, so fills (1.25 × 1/6) = 5/24 per hour. Pipe C empties 1/12 per hour. Combined rate = 1/6 + 5/24 - 1/12 = 4/24 + 5/24 - 2/24 = 7/24 per hour. 83.33% = 5/6. Time = (5/6) ÷ (7/24) = (5/6) × (24/7) = 20/7 hours.

Multiple choice

Two inlet pipes A and B can fill an empty cistern in 22 and 33 hours, respectively. They are switched on together but pipe B had to be closed 7 hours before the cistern was full. How many hours in all did it take the two pipes to fill the cistern?

  1. 15

  2. 16.2

  3. 4.2

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

Pipe A fills at 1/22 per hour, Pipe B at 1/33 per hour. Combined rate is 5/66 per hour. Pipe B operates 7 hours less than Pipe A. If total time is T hours, A works T hours and B works (T-7) hours. Work equation: T/22 + (T-7)/33 = 1. Multiplying by 66: 3T + 2(T-7) = 66, so 5T - 14 = 66, giving 5T = 80 and T = 16 hours. This confirms option D is correct.

Multiple choice

Three pipes A, B and C can fill an empty tank in 15, 10 and 5 minutes respectively. When the tank is empty, all three pipes are opened simultaneously. A chemical solution P comes out of A. What is the amount of solution P in the tank after 2 minutes?

  1. 9/11

  2. 12/11

  3. 6/11

  4. 2/11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Pipe rates: A = 1/15 per min, B = 1/10 per min, C = 1/5 per min. Combined rate = 1/15 + 1/10 + 1/5 = 11/30 per min. In 2 minutes, tank fills to 22/30 = 11/15. Pipe A contributes 2/15 of solution P. Proportion of P = (2/15)/(11/15) = 2/11 of the total solution in the tank.

Multiple choice

Two inlet pipes A and B can fill an empty tank in 12 and 15 hours respectively, while a drain pipe C can empty full tank in 20 hours. How much time it will take to completely fill the tank if drain pipe was opened after 5 hours?

  1. 10

  2. 7.5

  3. 8

  4. 6.67
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First 5 hours only A and B are open, filling at rate 1/12 + 1/15 = 3/20 tank per hour, so 5*(3/20) = 3/4 tank fills. Remaining 1/4 tank is filled by all three pipes at rate 1/12 + 1/15 - 1/20 = 1/10 tank per hour, taking (1/4)/(1/10) = 2.5 hours. Total time = 5 + 2.5 = 7.5 hours.

Multiple choice

Pipe A can fill an empty tank in 1.5 hours, while pipe B can empty a filled tank in 2.4 hours. When the tank is empty, pipe A is turned on and closed for one hour. Now pipe B is opened for one hour to drain the water from the tank and then closed. Pipes in the tank are alternately opened and closed for one hour each time. How long will it take to fill the tank completely?

  1. 4.75 hours

  2. 6.375 hours

  3. 7 hours

  4. 8 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills at 1/1.5 = 2/3 tank per hour. Pipe B empties at 1/2.4 = 5/12 tank per hour. In each 2-hour cycle (1 hr filling + 1 hr emptying), net fill = (2/3 - 5/12) = (8/12 - 5/12) = 3/12 = 1/4 tank. After 3 full cycles (6 hours), tank is 3/4 full. Hour 7 (filling): adds 2/3, making 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 5/12 - overflow means tank fills during this hour. Tank needs 1/4 more. Time needed = (1/4) / (2/3) = 3/8 hour = 0.375 hours. Total = 6 + 0.375 = 6.375 hours.

Multiple choice

A water tank is filled in 3 hours by 3 pipes P, Q and R working together. The pipe P is 3 times as fast as pipe Q is 4 times as fast as pipe R. Then in how much time will pipe R take to fill the tank alone?

  1. 40 hrs

  2. 51 hrs

  3. 55 hrs

  4. 44 hrs

  5. Can’t determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let R's rate = 1 unit tank/hr. Then Q's rate = 4×R = 4 units/hr, and P's rate = 3×Q = 12 units/hr. Combined rate = 1+4+12 = 17 units/hr. Time together = 1/17 hr/tank = 3 hours, so 1 tank = 51 hours. R alone takes 51/1 = 51 hours. Option A (40), C (55), D (44), and E are incorrect.

Multiple choice

Pipes A and B can fill a tank in 10 hours and 40 hours, respectively. C is an outlet pipe attached to the tank. If all the three pipes are opened simultaneously, it takes 80 minutes more time than what A and B together take to fill the tank. A and B are kept opened for 7 hours and then closed and C was opened. C will now empty the tank in:

  1. 42 hours

  2. 45.5 hours

  3. 49 hours

  4. 38.5 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A and B together fill at 1/10 + 1/40 = 1/8 tank per hour, taking 8 hours. With C open, time is 8 hours 80 minutes = 28/3 hours, so combined rate is 3/28 tank/hour. C's emptying rate = 1/8 - 3/28 = 1/56 tank/hour. After A and B fill for 7 hours, tank has 7/8 water. C empties 7/8 ÷ 1/56 = 49 hours. Option A (42) would require C's rate as 1/48, and Option B (45.5) is not consistent with the calculations.

Multiple choice

Pipe A can fill an empty tank in 5 hours and pipe B takes 6.25 hours to fill it. When the tank was empty, both pipes were opened together, but after some time, pipe B was closed, which took 3.4 hours to fill the tank. For how many hours was pipe B opened?

  1. 2

  2. 1

  3. 2.5

  4. 1.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe A fills at 1/5 tank per hour. Pipe B fills at 1/6.25 = 4/25 tank per hour. Combined rate = 1/5 + 4/25 = 9/25 per hour. Let both pipes be open for t hours. Then A alone works for (3.4 - t) hours. Equation: (9/25)t + (1/5)(3.4 - t) = 1. Solving: (4/25)t = 0.32, so t = 2 hours. Option A is correct.

Multiple choice

Two entrance pipes can fill a tank in 10 and 12 hours respectively and one drainage pipe can empty 80 gallons of water per hour. All the three pipes working together can fill an empty tank in 20 hours. What is the capacity (in gallons) of the tank?

  1. 600

  2. 1200

  3. 1800

  4. 900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the tank capacity be C gallons. The two inlet pipes fill at C/10 and C/12 gallons per hour. The drainage pipe empties 80 gallons/hour. Working together, their net rate is (C/10 + C/12 - 80) gallons/hour. Since they fill the tank in 20 hours: C/20 = C/10 + C/12 - 80. Solving: C/20 = 11C/60 - 80, so 3C = 11C - 4800, giving 8C = 4800, hence C = 600 gallons.

Multiple choice

Two pipes A and B can fill the tank in 16 hours and 20 hours respectively. If both the pipes are simultaneously opened in an empty tank, what part of the tank is filled after 8 hours?
  1. $3/5$
  2. $9/10$
  3. $3/10$
  4. $9/12$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/16 of the tank per hour, and pipe B fills 1/20 per hour. Together they fill 1/16 + 1/20 = 9/80 per hour. In 8 hours, they fill 8 × (9/80) = 9/10 of the tank. Alternatively: in 8 hours, A fills 8/16 = 1/2 and B fills 8/20 = 2/5, so total = 5/10 + 4/10 = 9/10.

Multiple choice

Two pipes P and Q can fill a tank in 8 hours. If only pipe P is open then it would take 4 hours longer to fill the tank. Find how much longer it would take if only pipe Q is open.

  1. 16 hr.

  2. 12 hr.

  3. 10 hr.

  4. 8 hr.

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

Combined rate: 1/8 tank per hour. Let P's rate = 1/x, Q's rate = 1/y. Given: P takes 4 hours longer than combined time, so x=12 hours. P's rate = 1/12. Q's rate = (1/8)-(1/12)=1/24. Therefore Q alone takes 24 hours, which is 16 hours longer than the combined 8 hours.