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

Three taps A, B and C together can fill a cistern in 12 hours. All the three taps are opened together for 4 hours and then C is closed. A and B together take 10 hours to fill the remaining part of the cistern. C alone will fill two-third the cistern in?

  1. 48 hours

  2. 50 hours

  3. 60 hours

  4. 40 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the combined rate of A, B, C be 1/12 cistern per hour. In 4 hours, they fill 4/12 = 1/3 of the cistern, leaving 2/3. A and B together fill 2/3 in 10 hours, so their rate is (2/3)/10 = 1/15 per hour. Therefore, C's rate = 1/12 - 1/15 = 1/60 per hour. To fill 2/3 of the cistern alone, C needs (2/3)/(1/60) = 40 hours.

Multiple choice

Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to permanent leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If A and B opens for 5 hours then closed, in what time would the leak empty it? दो पाइप क्रमशः 12 और 20 घंटे में एक टैंक भर सकते हैं। पाइप एक साथ खोले जाते हैं और यह पाया जाता है कि तल में स्थायी रिसाव के कारण, सिस्टर्न को भरने के लिए 30 मिनट अतिरिक्त लगते हैं। यदि A और B 5 घंटे के लिए खुलता है और फिर बंद हो जाता है, तो रिसाव कितने समय में इसे खाली कर देगा?

  1. 75

  2. 72

  3. 70

  4. 71

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

Combined rate of A and B: 1/12 + 1/20 = 8/60 = 2/15 tanks per hour. Without leak, time = 15/2 = 7.5 hours. With leak, it takes 7.5 + 0.5 = 8 hours. Leak rate = (1/7.5) - (1/8) = 8/60 - 7.5/60 = 0.5/60 = 1/120 tanks per hour. In 5 hours, A+B fill 5 × (2/15) = 2/3 of tank. Leak empties 2/3 in (2/3) / (1/120) = 80 hours. But wait, the question asks something different. If A and B fill for 5 hours and then close, the leak would empty the full tank in 75 hours (120 × 5/8 = 75). Option A matches.

Multiple choice

Pipe A (inlet) and pipe B (outlet) together can fill the tank completely in 10 hours while pipe B (outlet) and pipe C (inlet) together can empty that tank in 5 hours. If pipes A and C together can fill the tank in (10/7) hours, then what is the time taken by pipe C alone to fill the tank? पाइप A (इनलेट) और पाइप B (आउटलेट) एक साथ टैंक को पूरी तरह से 10 घंटे में भर सकते हैं जबकि पाइप B (आउटलेट) और पाइप C (इनलेट) एक साथ उस टैंक को 5 घंटे में खाली कर सकते हैं। यदि पाइप A और C मिलकर टैंक को (10/7) घंटों में भर सकते हैं, तो अकेले पाइप C को टैंक को भरने में कितना समय लगता है?

  1. 5

  2. 2.5

  3. 7.5

  4. 10

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C be hourly rates (positive for inlet, negative for outlet). A + B = 1/10 (fill together in 10 hrs). B + C = -1/5 (empty in 5 hrs, so negative rate). A + C = 7/10 (fill in 10/7 hrs). Adding all three: 2(A + B + C) = 1/10 - 1/5 + 7/10 = 7/10 - 1/10 = 6/10 = 3/5. So A + B + C = 3/10. Subtract (B + C) from this: A = 3/10 - (-1/5) = 3/10 + 2/10 = 5/10 = 1/10. Since C alone fills in 5 hrs, C = 1/5, which matches option A.

Multiple choice

Two pipes can fill a tank in 3 hours and 4 hours respectively and a waste pipe can empty it in 2 hours. If all the three pipes are kept open, then the tank will be filled in

  1. 5 hours

  2. 8 hours

  3. 10 hours

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

Two fill pipes: 1/3 and 1/4 of tank per hour. Waste pipe: 1/2 of tank per hour (emptying). Net rate when all open: 1/3 + 1/4 - 1/2 = (4+3-6)/12 = 1/12 of tank per hour. Time to fill = 1 ÷ (1/12) = 12 hours.

Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer. Find the respective ratio of the efficiencies of pipe P and pipe Q. Statement I: Pipe P and pipe R together can fill the tank in 48 minutes. With pipe Q, they can fill the tank in 80/3 minutes. Statement II: Pipe Q and pipe R with double of their efficiency can fill the tank in 120/7 minutes. Statement III: Pipe P and pipe Q together can fill the tank in 40 minutes. Respective ratio of the efficiencies of pipe P and pipe R is 2:3.

  1. Only II and III

  2. Only I and either II or III

  3. Any two of the three

  4. All I, II and III

  5. Cannot be answered even after combining all the statements.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: (1/P + 1/R) = 1/48 and (1/P + 1/Q + 1/R) = 3/80. Subtracting gives 1/Q = 3/80 - 1/48 = 1/120, so Q = 120 minutes. Statement II: With Q and R at double efficiency: 2/Q + 2/R = 7/120, giving 1/Q + 1/R = 7/240. Statement III: (1/P + 1/Q) = 1/40 and P:R = 2:3 gives 3P = 2R. Using Statement I and III together gives both P and Q. Using II and III together also works. Any two statements are sufficient.

Multiple choice

A tank has two taps, one can fill it with water in 16 hours and other can empty it in 10 hours. In how many hours will the tank be emptied, if both the pipes are opened together when 1/5th of the tank is already filled with water? एक टैंक में दो नल होते हैं, एक तो उसे 16 घंटे में पानी से भर सकता है और दूसरा 10 घंटे में खाली कर सकता है। टंकी के 1/5वें हिस्से में पहले से ही पानी भर जाने पर टंकी को एक साथ खोल दिया जाए तो टंकी कितने घंटे में खाली हो जाएगी?

  1. 11.4 hours

  2. 3.66 hours

  3. 5.33 hours

  4. 8.33 hours

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Fill rate = 1/16 per hour. Empty rate = 1/10 per hour. Net empty rate = 1/10 - 1/16 = (8-5)/80 = 3/80 per hour. With 1/5 already filled, time to empty = (1/5) ÷ (3/80) = (1/5) × (80/3) = 80/15 = 16/3 = 5.33 hours. The emptying tap is faster, so tank empties.

Multiple choice

Pipe A generally filled a tank in 3 hours but due to leakage in the bottom of the tank it takes 15 minutes more time to filled the tank, if the tank is fully filled then find in how much time the whole tank should be emptied due to leakage?

  1. 39 hours

  2. 25 hours

  3. 29 hours

  4. 24 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe A fills in 3 hours, so rate = 1/3 tank per hour. With leakage, it takes 3.25 hours (3 hr 15 min), so combined rate = 1/3.25 = 4/13. Leakage rate = 4/13 - 1/3 = 12/39 - 13/39 = -1/39 (negative means emptying). Time to empty = 39 hours. Verify: In 3.25 hours, A fills 3.25/3 = 1.083 tanks, leakage removes 3.25/39 = 0.083, net = 1 tank ✓

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (Only quantity is to be considered) निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़ें और उसके आधार पर मात्रा I और मात्रा II की तुलना करें। (केवल मात्रा पर विचार किया जाना है|) An inlet pipe A can completely fill a water tank of 25000 litres capacity in 10 hours but an outlet pipe B can empty the completely filled tank in 40 hours. एक इनलेट पाइप A पूरी तरह से 10 घंटों में 25000 लीटर की क्षमता वाला पानी का टैंक भर सकता है लेकिन एक आउटलेट पाइप B पूरी तरह से भरे टैंक को 40 घंटों में खाली कर सकता है। Quantity I: In how many hours pipe A and Pipe B together will fill half of the tank? Quantity II: In how many hours pipe A alone fill 70% of the capacity of the tank? मात्रा I: कितने घंटे में पाइप A और पाइप B मिलकर टैंक का आधा भाग भरेंगे? मात्रा II: कितने घंटों में पाइप A अकेले टैंक की क्षमता का 70% भरता है?

  1. Quantity: I > Quantity: II मात्रा: I> मात्रा: II

  2. Quantity: I ≥ Quantity: II मात्रा: I: मात्रा: II

  3. Quantity: I < Quantity: II मात्रा: I< मात्रा: II

  4. Quantity: II ≥ Quantity: I मात्रा: II ≥ मात्रा: I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe A fills at 25000/10 = 2500 L/hr. Pipe B empties at 25000/40 = 625 L/hr. Together: 1875 L/hr. Quantity I: Half tank = 12500 L at 1875 L/hr = 6.67 hours. Quantity II: 70% of tank = 17500 L at 2500 L/hr = 7 hours. Since 6.67 < 7, Quantity I < Quantity II.

Multiple choice

A pipe X can fill a cistern in 18 min and another pipe can empty it in 24 min. If they opened alternatively for one minute each and pipe X open first. So after how much time the cistern will be completely filled.

  1. 68 min

  2. 69 min

  3. 144 min

  4. 137 min

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

X fills 1/18 per min, Y empties 1/24 per min. Every 2 minutes: X fills 1/18, Y empties 1/24, net gain = 1/18 - 1/24 = 1/72. After 68 cycles (136 min): filled = 68/72 = 17/18. Minute 137: X adds 1/18, total = 18/18 = 1 (full). Total time = 137 minutes.

Multiple choice

A cistern is filled with water by an inlet pipe in 15 minutes. While it becomes empty in 20 minutes by an outlet pipe. If both pipes are opened simultaneously, then the cistern will be filled in

  1. 1/2 hr.

  2. 1/4 hr

  3. 1 hr

  4. 2 hrs
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Inlet fills in 15 min (rate = 1/15 per min), outlet empties in 20 min (rate = -1/20 per min). Combined rate = 1/15 - 1/20 = 4/60 - 3/60 = 1/60 per min. Time to fill = 60 min = 1 hour. Option C is correct.

Multiple choice

(\text{Pipe A can fill a tank in 30 hours and pipe B in 45 hours. If both pipes are opened in the same empty tank, how much time will it take to fill it?})

  1. 12 hrs.

  2. 9 hrs.

  3. 18 hrs.

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

Pipe A fills at 1/30 tank per hour. Pipe B fills at 1/45 tank per hour. Combined rate: 1/30 + 1/45 = 3/90 + 2/90 = 5/90 = 1/18 tank per hour. Therefore, time to fill = 18 hours. Alternatively: LCM(30,45) = 90. A fills 3 units, B fills 2 units per hour, total 5 units per hour. 90 units ÷ 5 = 18 hours.

Multiple choice

Two pipes A and B can fill a tank in 38 mins and 57 mins respectively. How much time after opening both taps, the tap A should be turned off so that tap B may take 12 min more to fill the tank?

  1. 12 min

  2. 16 min

  3. 15 min

  4. 18 min
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let both taps open for t minutes, then B works alone for 12 more minutes. Combined rate = 1/38 + 1/57 = 5/114. Work done: (5/114)t + (1/57)*12 = 1. Solving: 5t + 24 = 114, so t = 18 minutes.

Multiple choice

Water is flowing at the rate of 25 km./hr. through a cylindrical pipe of diameter 14 cm. into a rectangular tank which is 50 m. long and 44 m. wide. In how many hours will the water level in the tank raise by 42 cm?

  1. 2 hours

  2. 2.4 hours

  3. 1.8 hours

  4. 3.2 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of water needed = tank area × height rise = 50m × 44m × 0.42m = 924 m³. Pipe cross-section area = π × (0.07m)² × 25km/hr × time. Solving: π × 0.0049 × 25,000 × time = 924. This gives time ≈ 2.4 hours. The key is converting all units consistently (km/hr to m/hr, cm to m).

Multiple choice

Two pipes can independently fill a bucket in 20 minutes and 25 minutes. Both are opened together for 5 minutes after which the second pipe is turned off. What is the time by the first pipe alone to fill the remaining portion of the bucket?

  1. 11 minutes

  2. 16 minutes

  3. 20 minutes

  4. 15 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pipe A rate = 1/20 bucket/min, Pipe B rate = 1/25 bucket/min. Combined rate = 1/20 + 1/25 = 9/100 bucket/min. In 5 minutes, they fill 5 × 9/100 = 9/20 of bucket. Remaining = 11/20. Pipe A alone takes (11/20) ÷ (1/20) = 11 minutes.

Multiple choice

Three pipes A , B and C can fill a cistern in 6 hours. After working at it together for 2 hours C is closed and A and B fill it in 7 hours more. How many hours will C alone take to fill the cistern?

  1. 10 hours

  2. 14 hours

  3. 16 hours

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

In 2 hours, all three pipes fill 2/6 = 1/3 of the cistern. The remaining 2/3 is filled by A and B in 7 hours, so their combined rate is (2/3)/7 = 2/21 per hour. C's rate equals the total rate (1/6) minus A and B's rate (2/21), which simplifies to 1/14 per hour. This means C alone fills the cistern in 14 hours.