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

A leak in the bottom of a tank can empty a full tank in 7 hours. An inlet pipe fills water in the tank at the rate of 2 litres per minute. When the tank is full, the inlet is opened and due to the leak, the tank is emptied in 10.5 hours. The capacity of the tank is

  1. 2520 litres

  2. 3760 litres

  3. 2836 litres

  4. 2250 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Leak rate = 1/7 tank/hr. Let inlet rate be I. Net rate = I - 1/7 = -1/10.5 = -1/(21/2) = -2/21. I = 1/7 - 2/21 = 3/21 - 2/21 = 1/21. Inlet fills 1/21 tank per hour. Inlet rate = 2 L/min = 120 L/hr. 1/21 capacity = 120 L, so capacity = 120 * 21 = 2520 litres.

Multiple choice

A cistern can be filled by taps A and B in 12 minutes and 16 minutes, respectively. When the tank is full, it can be emptied by a third tap C in 8 minutes only. If all the taps are left running at the same time, then the cistern will be filled in

  1. 20 minutes

  2. 24 minutes

  3. 36 minutes

  4. 48 minutes

  5. 54 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: A = 1/12, B = 1/16, C = -1/8. Combined rate = 1/12 + 1/16 - 1/8 = (4 + 3 - 6) / 48 = 1/48. The cistern fills in 48 minutes.

Multiple choice

Three pipes A, B and C are attached to a tank. A and B can fill it in 20 and 30 minutes, respectively, while C can empty it in 15 minutes. If A, B and C are kept open successively for 1 minute each, how soon will the tank be filled if pipe A is opened first?

  1. 167 minutes

  2. 160 minutes

  3. 157 minutes

  4. 155 minutes

  5. 172 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A fills 1/20, B fills 1/30, C empties 1/15. Net rate per 3 minutes = 1/20 + 1/30 - 1/15 = 3/60 + 2/60 - 4/60 = 1/60. The tank fills 1/60 every 3 minutes. To avoid overfilling, consider the last cycle. After 164 minutes (approx), the tank is near full. Following the sequence, it fills at 167 minutes.

Multiple choice

Three pipes A, B and C can fill a tank in 5 hours. After working at it together for 3 hours, C is closed and A and B can fill the remaining part in 6 hours. The number of hours taken by C alone to fill the tank is

  1. 10.5 hours

  2. 12 hours

  3. 8 hours

  4. 7.5 hours

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

Let the total work be 1 unit. Combined rate of A+B+C = 1/5. In 3 hours, they complete 3/5 of the work. Remaining work = 2/5. A and B complete this in 6 hours, so their combined rate (A+B) = (2/5) / 6 = 1/15. Rate of C = (A+B+C) - (A+B) = 1/5 - 1/15 = 2/15. Time for C = 1 / (2/15) = 7.5 hours.

Multiple choice

There are two pipes in a cistern. One pipe can fill it with water in 32 hours, while the other pipe can empty it in 20 hours. How much time would it take to completely empty the cistern if both the pipes are opened together when 3/4th of the cistern is already full of water?

  1. 20 hours

  2. 24 hours

  3. 40 hours

  4. 36 hours

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

Rate of filling = 1/32. Rate of emptying = 1/20. Net rate = 1/32 - 1/20 = (5 - 8) / 160 = -3/160. The cistern is 3/4 full, so we need to remove 3/4 of the total volume. Time = (3/4) / (3/160) = (3/4) * (160/3) = 40 hours.

Multiple choice

Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 8:00 am and pipe B at 9:00 am, at what time will the pool be full?

  1. 15:00

  2. 17:00

  3. 18:00

  4. 19:00

  5. 20:00
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe A fills 1/4 per hour. Pipe B empties 1/6 per hour. From 8:00 to 9:00, A fills 1/4. At 9:00, remaining is 3/4. Net rate = 1/4 - 1/6 = 1/12 per hour. Time to fill remaining = (3/4) / (1/12) = 9 hours. 9:00 + 9 hours = 18:00.

Multiple choice

Two pipes A and B can fill a tank in 12 minutes and 16 minutes, respectively. Both are kept open for 'n' minutes and then B is closed. A fills the rest of the tank in 5 minutes. The value of n is

  1. 4

  2. 5

  3. 2

  4. 3

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

Pipe A fills 1/12 per minute and B fills 1/16 per minute. Together they fill (1/12 + 1/16) = 7/48 per minute. For n minutes, they fill 7n/48. A then fills the remaining part in 5 minutes, which is 5/12. Equation: 7n/48 + 5/12 = 1. Solving for n gives 7n/48 = 7/48, so n = 4.

Multiple choice

Mr. Mittal has a bath tub, to which two pipes, one for hot water and one for cold water, are attached. The hot water pipe can fill the tank in 8 hr and the cold water pipe can fill the tank in 12 hr. There is an outlet pipe which can empty the tank in 6 hr. The hot water and cold water pipes are open all the time, but the outlet pipe is opened after every two hours for one hour, and then closed again for the next two hours. How much time will the bath tub take to be completely filled with water?

  1. 3 hr and 12 min

  2. 6 hr and 12 min

  3. 5 hr and 16 min

  4. 6 hr and 24 min

  5. 8 hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Hot pipe fills 1/8 per hr, cold pipe fills 1/12 per hr. Net fill rate = 1/8 + 1/12 = 5/24 per hr. With outlet open, rate = 5/24 - 1/6 = 1/24 per hr. In 3-hour cycles (2 hrs fill, 1 hr empty), net fill = (5/24 * 2) - (1/6 * 1) = 5/12 - 2/12 = 3/12 = 1/4. After 6 hours (2 cycles), tank is 1/2 full. In the next 2 hours, it fills 5/12, total 11/12. Remaining 1/12 takes (1/12) / (5/24) = 2/5 hours = 24 minutes. Total time = 6 hr + 24 min.

Multiple choice

Pipe A can fill a tank in 4 hours and pipe B can fill the same tank in 5 hours. If t is the time (in hours) that both pumps take to fill the tank, which of these equations could be used to find t?

  1. 4t + 5t = 1

  2. t/4 + t/5 = 1

  3. t/(4 + 5) = 1

  4. (4 + 5)/t = 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/4 of the tank per hour, and Pipe B fills 1/5 of the tank per hour. Together, they fill (1/4 + 1/5) of the tank per hour. Over t hours, the total work done is t * (1/4 + 1/5) = 1, which simplifies to t/4 + t/5 = 1.

Multiple choice

A pipe can fill a tank in 20 minutes and another pipe can fill it in 30 minutes. A person opens both the pipes simultaneously. When the tank should have been full, he finds that the drain pipe is open. He then closes the drain pipe and after three minutes, the tank is full. In how much time can the drain pipe empty the tank?

  1. 50 min

  2. 48 min

  3. 44 min

  4. 38 min

  5. 60 min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/20 per min, Pipe B 1/30 per min. Combined = 1/12 per min. In 12 mins, they fill 1 tank. If drain pipe D is open, net rate = 1/12 - 1/D. After 12 mins, they filled (1/12 - 1/D)*12. Then D closes, and A+B fill the rest in 3 mins: (1/12)*3 = 1/4. Total = 1. Solving gives D = 48.

Multiple choice

Two inlet pipes A and B can fill a tank in 24 hours and 30 hours, respectively. An outlet pipe C can empty the tank in 60 hours. The pipe C is continuously open and the pipes A and B work on alternate hours, starting with A. How much time does it take to fill the tank?

  1. 36 hours

  2. 48 hours

  3. 40 hours

  4. 24 hours

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

A fills 1/24, B fills 1/30, C empties 1/60. In 2 hours (A+B), net work is (1/24 - 1/60) + (1/30 - 1/60) = 1/40 + 1/60 = 5/120 = 1/24. It takes 24 cycles of 2 hours to fill, so 48 hours.

Multiple choice

A cylindrical overhead tank is filled by two pumps, P1 and P2. P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours. There is a pipe, P3, which can empty the tank in 8 hours. The supervisor of the tank, before going somewhere, opens both the pumps simultaneously and also sets a timer to open P3 when the tank is half filled so that the tank is exactly filled up by the time he is back. Due to a technical fault, P3 opens when the tank is one-third filled. What percent of the tank is still empty if the supervisor comes back as per plan?

  1. 25%

  2. 12%

  3. 10%

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

P1+P2 fill rate = 1/8 + 1/12 = 5/24. P3 empty rate = 1/8. When P3 opens, net rate = 5/24 - 1/8 = 2/24 = 1/12. The tank is 1/3 full, so 2/3 remains. Time to fill 2/3 at 1/12 rate is 8 hours. Total time = (1/3)/(5/24) + 8 = 1.6 + 8 = 9.6 hours. At 9.6 hours, the tank is full. If P3 opened at 1/2, it would have been full. The fault causes 10% empty.