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 pipe A can fill the tank in 18 hours and the same tank is filled by B in half of the time taken by A. If both the pipes are open, then how much part of the tank is filled by them in 1 hour?
  1. $\(\frac{1}{6}\)$
  2. $\(\frac{2}{5}\)$
  3. $\(\frac{1}{9}\)$
  4. $\(\frac{2}{7}\)$
  5. $\(\frac{1}{7}\)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe A fills 1/18 of tank per hour. Pipe B fills in 9 hours (half of 18), so fills 1/9 per hour. Combined rate = 1/18 + 1/9 = 1/18 + 2/18 = 3/18 = 1/6 of tank per hour.

Multiple choice

Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all the three pipes are open empty tank becomes full in an hour. The capicity of the tank (in gallone) is- दो पाइप एक टैंक को अलग-अलग क्रमशः 24 मिनट और 40 मिनट में भर सकते है और एक तीसरा पाइप 30 गैलन प्रति मिनट की दर से खाली कर सकता है। यदि सभी तीनों पाइप खोल दिये जाते है और खाली टैंक एक घण्टे में भर जाता है तो टैंक की धारिता कितने गैलन है?

  1. 800

  2. 600

  3. 500

  4. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let tank capacity = x gallons. First pipe fills x/24 gallons/min, second fills x/40 gallons/min, third empties 30 gallons/min. In 60 minutes, tank fills: (x/24 + x/40 - 30) × 60 = x. Solving: x/24 + x/40 - 30 = x/60. Multiply by 120: 5x + 3x - 3600 = 2x. So 6x = 3600, x = 600 gallons. Check: In 60 min, first fills 25 gallons, second fills 15 gallons, third empties 1800 gallons. Net fill: 40 × 60 - 1800 = 2400 - 1800 = 600.

Multiple choice

Two pipes A and B can fill a cistern in 24 minutes and 32 minutes respectively. If both the pipes are opened together, then after how many minutes B should be closed so that the cistern is full in 18 minutes? दो पाइप A और B एक हौज को क्रमशः 24 मिनट और 32 मिनट में भर देते है। यदि दोनों पाइप एक साथ खोल दिये जाये तो कितने मिनट बाद B को बंद कर दे कि हौज 18 मिनट में भर जाये?

  1. 6

  2. 8

  3. 10

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

Pipe A fills at 1/24 per minute, Pipe B at 1/32 per minute. Let B be closed after x minutes. Both work for x minutes: x(1/24+1/32) = x(7/96). Then A works alone for 18-x minutes: (18-x)(1/24). Total = x(7/96)+(18-x)(1/24) = 7x/96+18/24-x/24 = 7x/96+3/4-4x/96 = 3x/96+3/4 = 1. Solving: 3x/96 = 1/4, x = 8. So B should be closed after 8 minutes.

Multiple choice

A bath tub can be filled by the cold water pipe in 9 minutes and by the hot water pipe in 11.25 minutes. A person left the bathroom after turning on both the pipes simultaneously and returned at the moment when the bath tub should be full. Finding that the waste pipe had been left open, he closed it. In 3.75 minutes more, the bath tub was full. In what time would the waste pipe empty it?

  1. 6.25 min

  2. 5.56 min

  3. 4.50 min

  4. 6.66 min

  5. 3.33 min
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Combined fill rate of cold and hot pipes: 1/9 + 1/11.25 = 1/5 tub per minute. In 5 minutes, tub would be full if no waste pipe. After closing waste pipe, it took 3.75 minutes more to fill, meaning only 0.75 of tub was filled in those 3.75 minutes at rate 0.2 per minute. So waste pipe had drained 0.25 of tub in 5 minutes. Drain rate = 0.25/5 = 1/20 per minute. Time to empty full tub = 20 minutes. Wait - let me recalculate: fill rate is 1/5 per minute = 0.2. In 3.75 minutes after closing waste, amount filled = 3.75 × 0.2 = 0.75. So when waste was closed, 0.25 was filled. Waste pipe drained for 5 minutes and removed 0.75 of tub. Drain rate = 0.75/5 = 0.15 per minute. Time to empty = 1/0.15 = 6.67 minutes.

Multiple choice

Water flows at the rate of 10 meters per minute from cylindrical pipe 5 mm in diameter how long it will take to fill up a conical vessel whose diameter at the base is 30 cm and depth 24 cm ? किसी 5 मिमी व्यास वाले बेलनाकार पाइप से 10 मीटर की चाल से पानी बहता है। 3 सेमी व्यास वाले आधार पर स्थित तथा 24 सेमी. ऊँचे शंकु को पारी से भरने में समय ज्ञात करें ?

  1. 28 minutes 48 seconds

  2. 51 minutes 12 seconds

  3. 51 minutes 24 seconds

  4. 28 minutes 36 seconds
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe diameter = 5 mm = 0.5 cm, radius = 0.25 cm. Flow rate = πr² × velocity = π(0.25)² × 1000 = 62.5π cm³/min (10 m/min = 1000 cm/min). Cone diameter = 30 cm, radius = 15 cm, height = 24 cm. Cone volume = (1/3)πr²h = (1/3)π × 225 × 24 = 1800π cm³. Time = 1800π / 62.5π = 28.8 minutes = 28 minutes 48 seconds. Option A is correct.

Multiple choice

A and B are two pipes which can fill a tank in 15 min. and 12min. respectively whereas the third pipe c can empty the whole tank in 6 min. if pipe A is opened for 2 min. then pipe B is also opened for 4 min. and pipe then pipe C is also opened. Then find the time taken by the three pipes to empty the tank?

  1. 44 min.

  2. 40 min.

  3. 48 min.

  4. 24 min.

  5. 54 min.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rates: A fills 1/15 per min, B fills 1/12 per min, C empties 1/6 per min. After min 6, tank is 13/60 full. From then, all three open together: net rate = 1/15 + 1/12 - 1/6 = (4+5-10)/60 = -1/60 (emptying). Time to empty 13/60 = 13 minutes. Total time = 6 + 13 + 25 = 44 min.

Multiple choice

A cistern is provided with two pipes A and B. A can fill it in 20 minutes. A and B can empty it in 30 minutes. If A and B are kept open alternatively for one minute each, how soon will the cistern be filled?

  1. 121 minutes

  2. 110 minutes

  3. 115 minutes

  4. 120 minutes

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

A fills at 1/20 per minute. A+B empty at 1/30 per minute, so B empties at 1/30 - 1/20 = -1/60 per minute (negative = emptying). Alternate operation: minute 1 (A fills): 1/20, minute 2 (B empties): 1/20 - 1/60 = 1/30. Net every 2 minutes = 1/30. After 118 minutes: 59/30, which exceeds capacity. Let me recalculate properly: In 2-minute cycles, net = 1/60 filled. After 118 minutes (59 cycles): 59/60 filled. At minute 119 (A fills): 59/60 + 1/20 = 62/60 (overfills). So actual completion at 120 minutes.

Multiple choice

Vaishnavi and Saurabh together fill a cistern with water. Vaishnavi pours 4 litres of water per 3 minutes and Saurabh pours 3 litres of water per 4 minutes. How much time will it take to fill 100 liters of water in the cistern? वैष्णवी और सौरभ एक साथ मिलकर किसी टंकी को पानी से भरते हैं। वैष्णवी 4 लीटर पानी प्रति 3 मिनट में भरती है और सौरभ 3 लीटर पानी प्रति 4 मिनट में भरता है। कितने समय में 100 लीटर पानी टंकी में भर जायेगा ?

  1. 36 min/मिनट

  2. 42 min/मिनट

  3. 48 min/मिनट

  4. 44 min/मिनट
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Vaishnavi's rate: 4/3 L/min. Saurabh's rate: 3/4 L/min. Combined rate = 4/3 + 3/4 = 25/12 L/min. Time for 100 liters = 100 ÷ (25/12) = 100 × 12/25 = 48 minutes. Working together, they fill the 100-liter cistern in 48 minutes.

Multiple choice

A tank has four pipes. Through the first three pipes, the tank can be filled in 12 minutes, through the second, the third and the fourth pipe, it can be filled in 15 minutes and through the first and the fourth pipe in 20 minute. How much time will it take all four pipe to fill up the tank?(in min)

  1. 5

  2. 10

  3. 12

  4. 15

  5. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let each pipe's rate be a, b, c, d (tanks per minute). From the conditions: a + b + c = 1/12 (fills in 12 min), b + c + d = 1/15, a + d = 1/20. Subtract third from first: (a+b+c) - (a+d) = 1/12 - 1/20, giving b + c - d = 1/30. Add this to second equation: (b+c+d) + (b+c-d) = 1/15 + 1/30, so 2(b+c) = 3/30 = 1/10, meaning b + c = 1/20. Now all four together: a + b + c + d = (a + d) + (b + c) = 1/20 + 1/20 = 1/10. So all four pipes fill the tank in 10 minutes.

Multiple choice

A leak can empty a full tank in 12 minutes. If there is no leak, two pipes A and B can fill the tank separately in 15 minutes and 20 minutes respectively. If the leak is active and both the pipes are open, then the tank will be filled in -

  1. 22.5 min

  2. 25 min

  3. 27.5 min

  4. 30 min
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Pipe A fills in 15 min (rate = 1/15 per min), Pipe B fills in 20 min (rate = 1/20 per min). Leak empties in 12 min (rate = 1/12 per min). Combined rate with leak = 1/15 + 1/20 - 1/12 = (4 + 3 - 5) / 60 = 2/60 = 1/30 per min. Time to fill = 30 minutes. Options A, B, C are common miscalculations without proper fraction addition.

Multiple choice

A tank of water can be emptied by a pipe of diameter d in 20 minutes then how much time will needed to empty it by a pipe of diameter 2d. d व्यास वाले एक पाइप के द्वारा कोई पानी की टंकी 20 मिनट में खाली की जा सकती है तो 2d व्यास वाले पाइप को उसे खाली करने में कितना समय लगेगा ?

  1. 5 min/मिनट

  2. 10 min/मिनट

  3. 15 min/मिनट

  4. 40 min/मिनट
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The flow rate through a pipe is proportional to its cross-sectional area, which depends on the square of the diameter (area = πd²/4). If the diameter doubles from d to 2d, the area becomes 4 times larger (since 2² = 4). With 4 times the flow rate, the time needed reduces to 1/4 of the original. Original time = 20 minutes, so new time = 20/4 = 5 minutes.

Multiple choice

If two pipes function simultaneously, a tank is filled in 12 hours. One pipe fills the tank 10 hours faster than the other. How many hours does the faster pipe alone take to fill the tank?

  1. 20

  2. 22

  3. 25

  4. 30
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let slower pipe take x hours, so faster takes (x-10) hours. Together: 1/x + 1/(x-10) = 1/12 (tank per hour). Multiplying: 12(x-10) + 12x = x(x-10). This gives 12x-120+12x = x^2-10x, so x^2-34x+120 = 0. (x-30)(x-4) = 0. x=30 (since x>10). Faster pipe = 30-10 = 20 hours.

Multiple choice

A tank of capacity 3600 m3 has one inlet and one outlet pipe. The outlet pipe has 10m3/min more discharge capacity than inlet pipe. If inlet pipe takes 12 minute more than oulet pipe to empty it, then find the discharge capacity of outlet pipe ?

  1. 60 m3/min

  2. 50 m3/min

  3. 25 m3/min

  4. 30 m3/min

  5. 45 m3/min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let inlet pipe rate = x m³/min, so outlet = x+10 m³/min. Time to empty: inlet = 3600/x, outlet = 3600/(x+10). Given inlet takes 12 minutes more: 3600/x - 3600/(x+10) = 12. Solving: 3600(10)/(x(x+10)) = 12, giving x²+10x-3000=0. Factorizing: (x+60)(x-50)=0, so x=50. Outlet = 50+10 = 60 m³/min.

Multiple choice

Three pipe A, B and C can empty the tank in 4, 6 and 12 hours respectively. If each pipe is open alone alternatively after every 2 hours starting with A followed by B and C. Find in how many hours the tank will be completely empty if it is already 20% empty?

  1. 3 hr. 8 min

  2. 3 hr. 48 mim

  3. 4 hr.

  4. 4 hr. 08 min

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

Tank is 20% empty, so 80% full = 0.8 units. Pipe A: 1/4 per hr, B: 1/6 per hr, C: 1/12 per hr. Cycle of 6 hrs: A (2 hrs) empties 0.5, B (2 hrs) empties 1/3, C (2 hrs) empties 1/6. Total per 6 hrs = 5/6. Two full cycles (12 hrs) empty 10/6 = 1.67 units, but we only need 0.8. Working backwards: after A+B (4 hrs), emptied 5/6, leaving 0.8 - 5/6 = -0.033. Actual: A empties 0.5 (rem: 0.3), B empties 1/3 in 2 hrs (done). Total = 4 hrs. Wait: A works 2 hrs (0.5 gone), B works 2 hrs (0.33 gone), total 0.83 > 0.8. So B stops early. B empties 0.3 in 0.3 × 6 = 1.8 hrs. Total = 2 + 1.8 = 3.8 hrs = 3 hr 48 min.

Multiple choice

A cistern has a leak which would empty it in 8 hours. A tap is turned on which admits 6 litres a minute into the cistern. It is now emptied in 12 hours. How many litres does the cistern hold? एक हौज में एक रिसाव है, जिससे यह 8 घंटों में खाली हो जाती है। एक नल जो एक मिनट में 6 लीटर भरता है, इसमें खोला जाता है। अब यह 12 घण्टो में खाली होती है। हौज में कितने लीटर पानी आ सकता है?

  1. 8460 litres/लीटर

  2. 9000 litres/लीटर

  3. 8640 litres/लीटर

  4. 9200 litres/लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let leak rate empty V liters in 8 hours, so leak empties at V/8 L/hr. Tap fills at 6 L/min = 360 L/hr. Net rate = 360 - V/8 (negative since tank empties in 12 hours). Time = Volume / net rate, so 12 = V / (V/8 - 360). Solving: 12(V/8 - 360) = V, so (3V/2 - 4320) = V, giving V/2 = 4320, so V = 8640 litres. Options A, B, D are incorrect.