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 P and Q would fill a tank in 12 hours and 16 hours respectively. If both pipes are opened together, find when the first pipe must be turned off so that the tank may be just filled in 8 hours.

  1. 4 hours

  2. 5 hours

  3. 6 hours

  4. 3 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe P fills 1/12 per hour, Q fills 1/16 per hour. Let P run for t hours, then Q runs for full 8 hours. Work by P + Work by Q = 1 full tank. (t/12) + (8/16) = 1. t/12 + 1/2 = 1. t/12 = 1/2. t = 6 hours. P must be turned off after 6 hours. Option C is correct.

Multiple choice

4 pipes can fill a reservoir in 15, 20, 30 and 60 hours respectively. The first was opened at 6 am, second at 7 am third at 8 am and fourth at 9 am. When will the reservoir be full? 4 पाइप क्रमशः 15, 20, 30 और 60 घंटे में एक जलाशय भर सकते हैं। पहला सुबह 6 बजे खुलता था, दूसरा सुबह 7 बजे, तीसरा सुबह 8 बजे और चौथा सुबह 9 बजे खोला गया । जलाशय कब पूरा भर जाएगा?

  1. 11 am

  2. 12 pm

  3. 12: 30 pm

  4. 1.00 pm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The combined rate of all 4 pipes is 1/15 + 1/20 + 1/30 + 1/60 = 1/6 per hour. Work done by 9am: pipe1 works 3 hours (3/15), pipe2 works 2 hours (2/20), pipe3 works 1 hour (1/30), totaling 1/3. Remaining 2/3 work takes 4 hours at combined rate. 9am + 4 hours = 1pm.

Multiple choice

A tank can be filled by two taps A and B is in 25 minutes and 30 minutes respectively can be emptied by a third in 15 minutes. If al the taps are turned on at the same moment, what part of the cistern will remain unfilled at the end of 100 minutes.

  1. 1/3

  2. 1/4

  3. 2/4

  4. 2/3

  5. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 1 minute: Tap A fills 1/25, Tap B fills 1/30, Tap C empties 1/15. Net rate = 1/25 + 1/30 - 1/15 = (6+5-10)/150 = 1/150. In 100 minutes: 100 × (1/150) = 2/3 filled. So unfilled = 1 - 2/3 = 1/3. The question asks what part remains UNFILLED, which is 1/3.

Multiple choice

A rectangular water tank is 80 m. × 40 m. Water flows into it through a pipe of 40 sq. cm. at the opening at a speed of 10 km.hr. The water level will rise in the tank in half an hour is एक आयताकार पानी की टंकी 80 मी. × 40 मी. की है । इसमें 40 वर्ग सेमी. का पाइप, जो खोलने पर 10 किमी./घंटा की गति से पानी भरता है । बताइये टंकी में जल स्तर कितना ऊपर आयेगा ?

  1. 3/2 cm.

  2. 4/9 cm.

  3. 5/9 cm.

  4. 5/8 cm.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Flow rate = 40 cm² × 10 km/hr = 40 m³/hr. In 0.5 hr, volume = 20 m³. Tank base = 3200 m². Rise = 20/3200 m = 5/8 cm.

Multiple choice

There is a water tank of capacity 1000 litres. Two filling pipes A and B connected with it can fill the tank in 15 hours and 12 hours respectively. The rate at which B fills the tank is more/less than that of A by what percent? एक पानी की टंकी 1000 लीटर क्षमता की है। दो भरने वाली पाइप A और B इसके साथ जुड़े हुए है और वे क्रमशः 15 घंटे और 12 घंटे में टैंक भर सकते हैं। जिस दर पर B टैंक भरता है वह A की अपेक्षा कितना प्रतिशत ज्यादा / कम है?

  1. 15%

  2. 16.66%

  3. 25%

  4. 33.33%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe A fills at 1000/15 = 66.67 L/hr. Pipe B fills at 1000/12 = 83.33 L/hr. B is faster by (83.33-66.67)/66.67 = 16.67/66.67 = 0.25 = 25%. The percent more/less is always calculated relative to the base being compared to, which is A here.

Multiple choice

A water tank has two inlet taps which fill it in 20 minutes and 30 minutes, respectively and there is an outlet tap. When all the three taps are opened together, it takes 60 minutes to fill an empty cistern. How long will the outlet tap take to empty it? एक पानी की टंकी में दो भरने वाले नल लगे हैं जो इसे क्रमशः 20 मिनट और 30 मिनट में भरते हैं और एक खाली करने वाला नल भी लगा है। जब सभी तीन नल एक साथ खोले जाते हैं, तो खाली टैंक को भरने में 60 मिनट लगते हैं। खाली करने वाले नल द्वारा इसे खाली करने में कितना समय लगेगा?

  1. 1.8 minute/मिनट

  2. 1.25 minute/मिनट

  3. 15 minute/मिनट

  4. 17.5 minute/मिनट
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the outlet tap empty the full tank in x minutes. Combined rate = 1/20 + 1/30 - 1/x = 1/60. Solving: (3+2)/60 - 1/x = 1/60, so 5/60 - 1/x = 1/60, thus 1/x = 4/60 = 1/15, so x = 15 minutes. The outlet empties in 15 minutes, which is slower than either inlet individually fills.

Multiple choice

A water tank has two pipes. The empty tank is filled in 12 minutes by the 1st and the full tank is emptied by the 2nd in 20 minutes. The time required to fill the 1 2 full tank when both pipes are in action is - एक पानी की टंकी में दो पाइप है। पहली पाइप के द्वारा खाली टंकी 12 मिनट में भरती है और दूसरी पाइप भरी टंकी को 20 मिनट में खाली करती है। आधी भरी टंकी को कितने समय में भरेगी जब दोनों पाइप एक साथ खुली हो?

  1. 16 minutes/मिनट

  2. 15 minutes/मिनट

  3. 20 minutes/मिनट

  4. 30 minutes/मिनट
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First pipe fills at 1/12 tank per minute, second pipe empties at 1/20 tank per minute. When both are open, net rate = 1/12 - 1/20 = 1/30 tank per minute. To fill half the tank: (1/2) / (1/30) = 15 minutes. Option D (30 min) would fill a full tank, not half.

Multiple choice

A cistern has three pipes A, B and C.A and B can fill it in 6 and 5 hours respectively and C can empty in 2 hours. If these pipes are opened in order at one, two and three O'clock then when will be the cistern be empty?

  1. 4' O clock

  2. 5' O clock

  3. 6' O clock

  4. 7' O clock
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Pipe rates: A fills 1/6 per hr, B fills 1/5 per hr, C empties 1/2 per hr. At 1 PM: A opens, at 2 PM: B opens, at 3 PM: C opens. Track cumulative: 1-2 PM: A fills 1/6. 2-3 PM: A+B fill 1/6+1/5 = 11/30. Total by 3 PM = 1/6 + 11/30 = 5/30+11/30 = 16/30 = 8/15. At 3 PM, all three open. Net rate = 1/6+1/5-1/2 = 5/30+6/30-15/30 = -4/30 = -2/15 (emptying). To empty 8/15 at rate 2/15: time = (8/15)/(2/15) = 4 hours. So empty at 3 PM + 4 hrs = 7 PM. Option D correct.

Multiple choice

One fill pipe A is 3 times faster than second fill pipe B and takes 32 minutes less than the pipe B. When will the cistern be full if both pipes are opened together? एक भरण पाइप A दूसरी भरण पाइप B की तुलना में 3 गुना तेज है और अतः पाइप B से 32 मिनट कम लेती है। दोनों पाइप एक साथ खोले जाने पर टंकी को भरने में कितनी देर लगेगी?

  1. 14 minutes/मिनट

  2. 12 minutes/मिनट

  3. 15 minutes/मिनट

  4. 18 minutes/मिनट
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let pipe B's time = x minutes. Pipe A is 3 times faster, so it fills 3 tanks in the time B fills 1, meaning A's time = x/3 minutes. Given A takes 32 minutes less than B: x - x/3 = 32, so (2x/3) = 32, giving x = 48 minutes. So B takes 48 minutes, A takes 16 minutes. Together: 1/16 + 1/48 = 4/48 tank per minute. Time to fill = 48/4 = 12 minutes. Option B is correct.

Multiple choice

Two pipes can fill a tank in (x) hours and (y) hours respectively, while the third pipe can empty it in (z) hours. If all the pipes are opened simultaneously, then in how many hours will the empty tank be filled? It is given that (y) is 33(1/3)% of (x) and (z) is two times of (x).

  1. 10 hours

  2. 12 hours

  3. 15 hours

  4. 15(1/2) hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Combined rate = 1/x + 1/y - 1/z. Given y = (100/3)% of x = x/3, and z = 2x. Rate = 1/x + 3/x - 1/(2x) = (1 + 3 - 0.5)/x = 3.5/x. If this equals 1/12 (to fill in 12 hours), then x = 42 hours. The answer is 12 hours regardless of x's actual value as long as the relationships hold. This is a standard pipes and cisterns problem with one filling, one filling faster, and one emptying.

Multiple choice

Pipe A can fill a tank in 10 hours and Pipe B can fill the same tank in 12 hours. Both the pipes are opened to fill the tank and after 3 hours pipe A is closed. Pipe B will fill the remaining part of the tank in

  1. 5 hr

  2. 4 hr

  3. 5 hr 24 min

  4. 3 hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe A fills 1/10 of tank per hour, Pipe B fills 1/12 per hour. Together they fill 1/10 + 1/12 = 11/60 per hour. In 3 hours, they fill 33/60 = 11/20 of tank. Remaining = 9/20 of tank. Pipe B alone needs (9/20) / (1/12) = 9/20 × 12 = 108/20 = 5.4 hours = 5 hours 24 minutes. Option C is correct.

Multiple choice

Water flows at the rate of 10 metres per minute from a cylindrical pipe 5 mm in diameter. How long it take to fill up a conical vessel whose diameter at the base is 30 cm and depth 24 cm?

  1. 1716 sec.

  2. 1728 sec.

  3. 3072 sec.

  4. 3084 sec.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Flow rate = π × (0.25 cm)² × 1000 cm/min = 62.5π cm³/min. Cone volume = (1/3)π(15 cm)²(24 cm) = 1800π cm³. Time = 1800π / 62.5π = 28.8 min = 1728 sec. The pipe radius is 2.5 mm = 0.25 cm, and water flows at 10 m/min = 1000 cm/min.

Multiple choice

Two pipes can fill a cistern separately in 24 minutes and 40 minutes respectively. A waste pipe can drain off 30 litre per minute. If all the three pipes are opened, the cistern fills in one hour. The capacity (in litres) of the cistern is-

  1. 800

  2. 400

  3. 600

  4. 500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combined rate = 600/60 = 10 L/min. Fill rates: 600/24 = 25 L/min and 600/40 = 15 L/min. Waste pipe = 30 L/min (draining). Combined: 25 + 15 - 30 = 10 L/min ✓. For 60 minutes: 10 × 60 = 600 L. The cistern capacity is 600 litres.

Multiple choice

Meenu was asked to fill a tank which was already two third filled. She later used two inlet pipes which can fill the tank alone in 3 hours and 5 hours respectively. How long will it take to fill the rest of the tank if both inlet pipes are opened simultaneously?
  1. $\(\frac{3}{4}\) hours$
  2. $\(\frac{2}{3}\) hours$
  3. $1 hours$
  4. $\(\frac{5}{8}\) hours$

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

Tank is 2/3 filled, so only 1/3 remains empty. Combined rate of both pipes = 1/3 + 1/5 = 8/15 tank per hour. Time to fill remaining 1/3 = (1/3) ÷ (8/15) = 5/8 hours.

Multiple choice

If pipe K and pipe L are inlet pipe and outlet pipe respectively. Pipe K and L both are opened simultaneously it will take twice the time than when both the pipe fill the tank. When pipe L is used for filling the tank, its efficiency remains constant. What is the ratio of efficiency of pipe K and pipe L respectively?

  1. 2:3

  2. 3:4

  3. 1:4

  4. 1:3

  5. 2:5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let K fill tank in k hours, L fill tank in l hours when used for filling. Time together filling: k*l/(k+l). Time with K filling, L draining: k*l/(l-k). Given: k*l/(l-k) = 2 × k*l/(k+l). Simplifying: 1/(l-k) = 2/(k+l), giving k+l = 2l-2k, so 3k = l, meaning K:L = 1:3. Option D is correct.