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

Passage

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities.

There are three inlet pipes P, Q and R and two outlet pipes S and T. The time take to fill the tank by P and Q together is same as the time taken by R alone. P takes (x + 6) hrs, Q takes (x+11) hrs and R takes (x+2) hrs to completely fill the tank and the outlet pipe S and T alone can empty the tank in 30 hrs and 20 hrs, respectively. Quantity I: Time taken to fill the tank when only inlet pipes P, R and outlet pipe T are opened. Quantity II: Time taken to fill the tank when all three inlet pipes and two outlet pipes are opened.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving for x using the given rates (1/(x+6) + 1/(x+11) = 1/(x+2)) yields x = 4. With x=4, P=10, Q=15, R=6, S=30, T=20. Quantity I (P, R, T) rate is 1/10 + 1/6 - 1/20 = (6+10-3)/60 = 13/60, time = 60/13 approx 4.6 hrs. Quantity II (P, Q, R, S, T) rate is 1/10 + 1/15 + 1/6 - 1/30 - 1/20 = (6+4+10-2-3)/60 = 15/60 = 1/4, time = 4 hrs. Thus, Quantity I > Quantity II.

Multiple choice

Passage

Directions: Study the paragraph and answer the question that follows. There were two similar tanks X and Y with five similar pipes P, Q, R, S and T. Pipes P, Q and R can fill the empty tank in 10 minutes, 15 minutes and 30 minutes respectively, while pipes S and T can empty the filled tank in 20 minutes and 30 minutes respectively. Tank X had no leaks, but tank Y had a leak, such as when pipe P was opened in the empty tank Y, it took 12 minutes to fill tank Y.

If pipe Q was opened into the empty tank Y, it could be filled in ______ minutes, while pipe R could fill the empty tank Y in _______ minutes. Which of the following options satisfies the two blanks in the question? A. 16, 32 B. 16, 48 C. 20, 60 D. 20, 80

  1. Only A

  2. Only B

  3. Only C

  4. Only D

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe P fills tank X in 10 min. In tank Y, it takes 12 min, implying a leak rate L = 1/10 - 1/12 = 1/60. Pipe Q fills in 15 min, so net rate in Y is 1/15 - 1/60 = 3/60 = 1/20 (20 min). Pipe R fills in 30 min, so net rate in Y is 1/30 - 1/60 = 1/60 (60 min).

Multiple choice

Passage

Directions: Study the paragraph and answer the question that follows. There were two similar tanks X and Y with five similar pipes P, Q, R, S and T. Pipes P, Q and R can fill the empty tank in 10 minutes, 15 minutes and 30 minutes respectively, while pipes S and T can empty the filled tank in 20 minutes and 30 minutes respectively. Tank X had no leaks, but tank Y had a leak, such as when pipe P was opened in the empty tank Y, it took 12 minutes to fill tank Y.

When pipes Q and S were simultaneously opened into the empty tank X, 40 gallons of liquid was filled in the tank after 12 minutes. This means that the tank had a capacity of _____ gallons and pipe S could empty it at a rate of _______ gallons per minute. Which of the following options satisfies the two blanks in the question? (A) 200, 10 (B) 240, 12 (C) 280, 15 (D) 320, 20

  1. Only A

  2. Only B

  3. Only C

  4. Only D

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

P fills in 10, Q in 15, R in 30. S empties in 20. Rate of Q = 1/15, Rate of S = -1/20. Net rate = 1/15 - 1/20 = 1/60. In 12 minutes, 12/60 = 1/5 of the tank is filled. If 1/5 capacity = 40 gallons, then capacity = 200 gallons. Pipe S rate = 1/20 of 200 = 10 gallons/min.

Multiple choice

Passage

In each of the following questions, a question & then two statements – I & II are given. You have to determine that the data provided in these statements is enough to answer the question or not. Study both the statement: निम्नलिखित प्रत्येक प्रश्न में एक प्रश्न और फिर दो कथन I और II दिए गए हैं। आपको यह निर्धारित करना है कि इन कथनों में प्रदान किया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों का अध्ययन करें:

If taps A, B and C are open simultaneously, how long will it take to fill the tank completely where C is out let pipe? यदि नल A, B और C एक साथ खुले हैं, तो टैंक को पूरी तरह से भरने में कितना समय लगेगा जहां C निकासी नल है? Statement I – When pipe A and B is open together the tank fill in 24 hr. Statement II – When pipe c is open it can empty the full tank in 30 hr. कथन I - जब पाइप A और B एक साथ खुले होते हैं तो टैंक 24 घंटे में भर जाता है। कथन II - जब पाइप c खुला होता है तो यह 30 घंटे में पूरे टैंक को खाली कर सकता है।

  1. Only Statement I alone. केवल कथन I

  2. Only Statement II alone. केवल कथन II

  3. Both Statements I and II together. दोनों कथन I और II एक साथ

  4. Neither Statement I nor II is sufficient. न तो कथन I और न ही II पर्याप्त है।

  5. Either Statement I or II. या तो कथन I या II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From Statement I, the combined filling rate of A and B is 1/24 tank per hour. From Statement II, pipe C's emptying rate is 1/30 tank per hour. When all three pipes are open simultaneously, the net rate is 1/24 - 1/30 = 1/120, meaning the tank fills in 120 hours. Neither statement alone is sufficient - both are required to solve the problem.

Multiple choice

Passage

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए।

Quantity I : A and B together can do a piece of work in 6 hours. A is 50% more efficient than B. In how many hours, A alone can complete the work? Quantity II : Pipes A and B individually can fill the empty tank in 10 hours and 20 hours respectively. Pipe C alone can fill the empty tank in 40 hours. Pipe A is opened at the start and after 2 hours pipe B is also opened. After 3 more hours pipe C is also opened. In how many hours the tank is filled completely? मात्रा I : A और B मिलकर एक काम को 6 घंटे में पूरा कर सकते हैं। A, B से 50% अधिक कुशल है। A अकेले कार्य को कितने घंटे में पूरा कर सकता है? मात्रा II : पाइप A और B अलग-अलग खाली टैंक को क्रमशः 10 घंटे और 20 घंटे में भर सकते हैं। पाइप C अकेले खाली टैंक को 40 घंटे में भर सकता है। पाइप A को प्रारंभ में खोला जाता है और 2 घंटे के बाद पाइप B को भी खोला जाता है। 3 घंटे और बाद पाइप C को भी खोल दिया जाता है। टंकी कितने घंटे में पूरी तरह भर जाती 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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Let B's efficiency = 2 units/hour, then A's = 3 units/hour (50% more). Combined = 5 units/hour. Total work = 5 × 6 = 30 units. A alone = 30/3 = 10 hours. Quantity II: A works 2 hours = 2/10 tank, A+B work 3 hours = 3(1/10 + 1/20) = 9/20 tank. Remaining = 1 - 2/10 - 9/20 = 9/20 tank. With A+B+C: rate = 1/10 + 1/20 + 1/40 = 7/40 per hour. Time for 9/20 = (9/20)/(7/40) = 18/7 ≈ 2.57 hours. Total = 5 + 2.57 = 7.57 hours. 10 hours > 7.57 hours, so Quantity I > Quantity II. Option A is correct.

Multiple choice

Passage

Each of the questions below consists of a question and three statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the three statements and give answer.

Find the time taken by pipe C to fill the tank? I. Pipe A, Pipe B and Pipe C together can fill a tank in 8 minutes. Efficiency of pipe A is double the efficiency of pipe D. II. Pipe A and pipe D together can complete the work in 10 days. III. Pipe B and pipe D together can complete the work in 12 days.

  1. Only I and III

  2. Only II and III

  3. All I, II and III

  4. Any two of the three

  5. I, II and III together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rates be a, b, c, d (in tanks per minute). From I: a+b+c = 1/8. From II: a+d = 1/10, so d = 1/10 - a. From III: b+d = 1/12. Substituting d from II into III: b + (1/10 - a) = 1/12, giving b = a - 1/60. From I: a + (a-1/60) + c = 1/8, so 2a + c = 1/8 + 1/60 = 17/120. We need all three statements to uniquely determine c, the rate of pipe C.

Multiple choice

Passage

Each of the questions below consists of a question and two statements I, and II 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.

Pipe M and N can fill a tank at the rate of 12 and 10 litre per minute respectively. There is a leakage also in the same tank. What is the capacity of the tank? Statement I : If M and N are opened simultaneously, the tank is filled in 5 hours 45 minutes and a leakage hole drains the pipe at the rate of 6 litres/minute. Statement II : Due to the leak the filled tank drains in 15 hours 20 minutes. If M and N are opened simultaneously, the tank is filled in 5 hours 45 minutes .

  1. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. If the data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. If the data in both statements I and II together are necessary to answer the question.

  5. If the data given in both statements I and II together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: Combined fill rate = 22 L/min (12+10-6 leakage). Time = 5h 45m = 345 min. Capacity = 22 × 345 = 7,590 litres. Statement I alone gives the capacity. Statement II: Leakage rate from draining time = 7590 / 920 min ≈ 8.25 L/min, but this requires knowing the capacity first. Both statements independently give the capacity (Statement II references the same fill time). So either statement alone is sufficient.

Multiple choice

Passage

Directions: Read the data given below carefully and answer the question. The data shows the volume and dimensions (length, breadth, and height) of four cuboidal tanks: A, B, C, and D. The data also depicts the time taken to fill or empty the tanks by inlet pipes X, Y, and the outlet pipe Z. 1. The breadth of tank D is 14 m. Tank Data: Tank Volume (m³) Dimensions: L × B × H (m) Time taken by pipe X to fill (hours) Ratio of time taken by pipe Y to fill and pipe Z to empty A 3,600 20 × 15 × ---- 10 2 : 3 B ----- 25 × 12 × 12 3 : 2 C 4,500 ---- × 6 × 15 18 1 : 4 D 16,800 14 × ---- × ---- ----- 3 : 5

In tank C, pipe X was opened for 9 hours and then closed. Pipes Y and Z were opened together for 2 hours and then both pipes were closed. After a total of 11 hours, approximately what volume of the tank remained empty (in cubic metres), considering that if both pipes X and Z were opened together, the tank would always be empty?

  1. 810 m3

  2. 750 m3

  3. 720 m3

  4. 680 m3

  5. 650 m³
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

Directions: Read the data given below carefully and answer the question. The data shows the volume and dimensions (length, breadth, and height) of four cuboidal tanks: A, B, C, and D. The data also depicts the time taken to fill or empty the tanks by inlet pipes X, Y, and the outlet pipe Z. 1. The breadth of tank D is 14 m. Tank Data: Tank Volume (m³) Dimensions: L × B × H (m) Time taken by pipe X to fill (hours) Ratio of time taken by pipe Y to fill and pipe Z to empty A 3,600 20 × 15 × ---- 10 2 : 3 B ----- 25 × 12 × 12 3 : 2 C 4,500 ---- × 6 × 15 18 1 : 4 D 16,800 14 × ---- × ---- ----- 3 : 5

Pipe Y alone can fill tank B in 36 hours. When all three pipes were opened for 1 hour, the volume of tank B filled was approximately 275 cubic metres. What is the height of tank B?

  1. 8.4 m

  2. 10.2 m

  3. 12.2 m

  4. 13.2 m

  5. 15.6 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Read the data given below carefully and answer the question. The data shows the volume and dimensions (length, breadth, and height) of four cuboidal tanks: A, B, C, and D. The data also depicts the time taken to fill or empty the tanks by inlet pipes X, Y, and the outlet pipe Z. 1. The breadth of tank D is 14 m. Tank Data: Tank Volume (m³) Dimensions: L × B × H (m) Time taken by pipe X to fill (hours) Ratio of time taken by pipe Y to fill and pipe Z to empty A 3,600 20 × 15 × ---- 10 2 : 3 B ----- 25 × 12 × 12 3 : 2 C 4,500 ---- × 6 × 15 18 1 : 4 D 16,800 14 × ---- × ---- ----- 3 : 5

When all three pipes were opened simultaneously, the volume of tank D filled in 1 hour was 5,600 cubic metres. Pipe Y alone can fill 25% of tank D in 5.25 hours. In how much time can pipe X fill 33% of tank D alone?

  1. 1.05 hours

  2. 2.05 hours

  3. 3.19 hours

  4. 3.62 hours

  5. 3.82 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Tank D volume = 16800. Pipe Y fills 25% (4200) in 5.25 hours, so rate Y = 800 m^3/hr. Ratio Y:Z = 3:5, so rate Z = 800 * (5/3) = 4000/3 m^3/hr. Total rate (X+Y-Z) = 5600 m^3/hr. X + 800 - 4000/3 = 5600. X = 4800 + 1333.33 = 6133.33. 33% of 16800 = 5544. Time = 5544 / 6133.33 = 0.904 hours. The option 1.05 is the closest.