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 individually can fill a tank in 10 hours and 12 hours, while a third pipe can empty the full tank in 20 hours. In how much time will the tank be filled, if all three pipes operate together?

  1. 8 hours

  2. 8 hours and 35 minutes

  3. 7 hours and 35 minutes

  4. 7 hours and 30 minutes

  5. 7 hours and 45 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rate = 1/10 + 1/12 - 1/20 = (6+5-3)/60 = 8/60 = 2/15. Time = 15/2 = 7.5 hours, which is 7 hours and 30 minutes.

Multiple choice

Two tanks are connected in parallel by two pipes A and B of identical friction factors and lengths. If the size of pipe A is double that of pipe B, then their discharges will be in the ratio of

  1. 2

  2. 4

  3. 5.66

  4. 2.83
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For pipes in parallel, the head loss is the same. Using the Darcy-Weisbach equation, head loss h is proportional to f * L * Q^2 / D^5. Since f and L are identical, Q^2 is proportional to D^5, so Q is proportional to D^2.5. If the diameter of A is double that of B, the ratio of discharges is 2^2.5, which is approximately 5.66.

Multiple choice

Four pipes are required to fill a tank. The tank can be filled by first 3 pipes in 12 minutes, by last 3 pipes in 15 minutes and by the first and the fourth pipes in 20 minutes. How much time will be taken by all the four pipes to fill the tank?

  1. 8 minutes

  2. 10 minutes

  3. 12 minutes

  4. 15 minutes

  5. 20 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let rates be r1, r2, r3, r4. r1+r2+r3 = 1/12, r2+r3+r4 = 1/15, r1+r4 = 1/20. Summing these: 2(r1+r2+r3+r4) = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5. So r1+r2+r3+r4 = 1/10. Time = 10 minutes.

Multiple choice

Pipe A can fill a tank in 8 hours and pipe B can fill it in 6 hours. If they are opened on alternate hours, with pipe A opened first, in how many minutes will the tank be full?

  1. 420

  2. 450

  3. 390

  4. 400

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

A fills 1/8 per hour, B fills 1/6 per hour. In 2 hours, they fill 1/8 + 1/6 = 7/24. In 6 hours (3 cycles), they fill 21/24. Remaining 3/24 = 1/8. Pipe A fills 1/8 in 1 hour. Total time = 6 + 1 = 7 hours = 420 minutes.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labeled (1) and (2). You have to decide whether the data given in the statements are sufficient for answering the question. How long will it take two pipes to empty or fill a tank that is 4/5th full? (1) Pipe P1 can fill the tank in 11 minutes. (2) Pipe P2 can empty it in 7 minutes.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both (1) and (2) together are sufficient, but none of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the time to fill/empty, we need the net rate. Statement 1 gives rate of P1, Statement 2 gives rate of P2. Together, we can find the net rate and solve the problem.

Multiple choice

It was observed that a red pipe takes 20 minutes to fill a bucket while a blue pipe took 30 minutes to fill the same bucket. How much time would it take to fill the bucket if both the pipes were used simultaneously?

  1. 10 minutes

  2. 11 minutes

  3. 12 minutes

  4. 13 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The red pipe fills 1/20 of the bucket per minute, and the blue pipe fills 1/30 of the bucket per minute. Together, they fill (1/20 + 1/30) = (3/60 + 2/60) = 5/60 = 1/12 of the bucket per minute. Thus, it takes 12 minutes to fill the bucket.

Multiple choice

Pipe P can fill a tank in 15 minutes, while pipe Q can fill the same tank in 30 minutes. Another pipe R can empty the tank in 20 minutes. In how many minutes will the tank be full if all the three pipes are opened together and after 10 minutes, pipe R is closed?

  1. 10 minutes

  2. 12 minutes

  3. 15 minutes

  4. 21 minutes

  5. 23 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P rate = 1/15, Q rate = 1/30, R rate = -1/20. Combined rate (P+Q+R) = (4+2-3)/60 = 3/60 = 1/20. In 10 minutes, they fill 10/20 = 1/2 of the tank. Remaining 1/2 is filled by P+Q at rate (1/15 + 1/30) = 3/30 = 1/10. Time = (1/2) / (1/10) = 5 minutes. Total time = 10 + 5 = 15 minutes.

Multiple choice

There is an inlet pipe at the top of a tank and an outlet pipe exactly in the middle of the tank. If both the taps are opened simultaneously, the tank is filled in 36 hours. If the inlet pipe alone can fill the tank in 30 hours and the outlet pipe is at the bottom of the tank, then how much time does it take to fill the tank? (Assume that there is no difference in the flow rate of water through the outlet pipe due to a change in its location)

  1. 36 hours

  2. 40 hours

  3. 42 hours

  4. 45 hours

  5. 48 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the total capacity be V. Inlet fills at V/30. With outlet at middle, it drains half the tank. The problem setup implies a rate calculation where the net flow leads to 42 hours.

Multiple choice

Two pipes A and B can fill a tank in 10 hr each, while a third pipe C can empty the tank in 8 hr. At 9 a.m, pipe A is opened and at 11 a.m, the other two pipes are opened. At what time will the tank be full?

  1. Between 6 p.m. and 7 p.m.

  2. Between 10 p.m. and 11 p.m.

  3. Between 9 p.m. and 10 p.m.

  4. Between 8 p.m. and 9 p.m.

  5. Between 7 p.m. and 8 p.m.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A fills 1/10 per hour. B fills 1/10 per hour. C empties 1/8 per hour. From 9 to 11, A fills 2/10 = 1/5. Remaining = 4/5. From 11 onwards, net rate = 1/10 + 1/10 - 1/8 = 2/10 - 1/8 = 1/5 - 1/8 = 3/40. Time to fill remaining = (4/5) / (3/40) = (4/5) * (40/3) = 32/3 = 10 hours 40 minutes. 11 a.m. + 10 hours 40 minutes = 9:40 p.m.

Multiple choice

Pipe A can fill a tank in 40 minutes. Pipe B can fill the same tank in 20 minutes. A leak at the bottom of the tank can empty the tank in 120 minutes. If both pipes are open and the tank is already half full, how long will it take to fill the tank?

  1. 7.5 minutes

  2. 5.5 minutes

  3. 6.5 minutes

  4. 7 minutes

  5. 9.5 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rate of Pipe A = 1/40. Rate of Pipe B = 1/20. Rate of leak = -1/120. Combined rate = 1/40 + 1/20 - 1/120 = (3+6-1)/120 = 8/120 = 1/15. Tank is half full, so 1/2 tank remains. Time = (1/2) / (1/15) = 15/2 = 7.5 minutes.

Multiple choice

Pipes P, Q and R can fill a tank in 24 hours. All the pipes are opened for 6 hours and then pipe P is closed. In another 30 hours, pipes Q and R fill the tank. How much time (in hours) does pipe P alone take to fill the tank?

  1. 30 hours

  2. 40 hours

  3. 60 hours

  4. 80 hours

  5. 65 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rates be p, q, r. p+q+r = 1/24. In 6 hours, they do 6/24 = 1/4 work. Remaining work = 3/4. Q+R do 3/4 work in 30 hours, so q+r = (3/4)/30 = 1/40. Then p = (p+q+r) - (q+r) = 1/24 - 1/40 = (5-3)/120 = 2/120 = 1/60. P takes 60 hours.

Multiple choice

Pipes X and Y can fill a tank in 8 hr and 12 hr, respectively. It happened that Shamu opened pipe X at 8 am and forgot to open pipe Y. After 120 min, he realised the mistake and then opened the other pipe. At what time will the tank be full?

  1. 11.36 pm

  2. 12.36 pm

  3. 1.36 pm

  4. 2.36 pm

  5. 3.36 pm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe X fills 1/8 per hour, Y fills 1/12 per hour. In 2 hours, X fills 2/8 = 1/4. Remaining 3/4. Combined rate = 1/8 + 1/12 = 5/24. Time = (3/4) / (5/24) = 18/5 = 3.6 hours (3 hours 36 minutes). Start time 10 am (after 2 hours), so 10 am + 3h 36m = 1:36 pm.