Quantitative Aptitude

Pipes and Cisterns

69 Questions

Pipes and cisterns problems test your understanding of inlet and outlet rates alongside time management. These questions are a staple in quantitative aptitude sections for SSC, banking, and railways. Mastering filling and emptying concepts is essential for scoring well.

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Pipes and Cisterns Questions

Multiple choice

Two tanks X and Y are filled to capacity with jet fuel. Tank X holds 600 gallons more than tank Y. If 100 gallons of fuel were to be pumped from each tank, tank X would then contain 3 times as much fuel as tank Y. What is the total amount of fuel in two full tanks (in gallons)?

  1. 1,400

  2. 1,200

  3. 1,000

  4. 900

  5. 800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the capacities of the two tanks are x and y respectively, it is given x = y + 600, and (x -100) = 3(y - 100). Substituting the value of x in the second equation, we get y + 500 = 3y - 300. So, 2y = 800, or y = 400. So, x = 1000. So, the total number of gallons in two full tanks = 1400.

Multiple choice

If a bacterial cell divides every minute, it takes 59 minutes to fill one half of the cup. How much time would it take to fill the full cup?

  1. 30 minutes

  2. 59 minutes

  3. 60 minutes

  4. 1 minute
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In 60 minutes the full cup will be filled. It is a known fact that when a bacteria divides by binary fission, it doubles itself in number. So, after the cup is half full, 1 more binary fission is required to fill the whole cup, as each bacteria in the half-filled cup is going to undergo binary fission and double itself.

Multiple choice

A leak in the bottom of the container can empty it in 6 hours. A pipe fills in the container at the rate of 4 litres/minute. When the container is full, the inlet in opened but due to the leak, the container is emptied in 8 hours. What is the capacity of the tank?

  1. 8590 litres

  2. 5000 litres

  3. 3750 litres

  4. 2440 litres

  5. 5760 litres
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

It is the correct answer. Solution : Combined 1 hour work of the inlet and leak is 1/8 hour. 1 hour work of inlet = 1/x 1/6 - 1/x = 1/8 x = 24 hour Rate of inlet = 4 litre/minute = 240 litre/hr Capacity of the container = 24*240=5760 litre

Multiple choice

Two pipes A and B can fill a tank in 6 hours. After working at it together for 2 hours, B is closed and A alone fills the remaining part in 8 hours. How many hours will B alone take to fill the tank?

  1. 12

  2. 16

  3. 8

  4. 4 hours

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

Part of tank filled by A and B in 2 hours = 2/6 = 1/3 So in 8 hours, part of the tank filled by A = 1 - 1/3 = 2/3 In 1 hour, part filled by A = 2/(3 * 8) = 1/12 Now, let B take X hours to fill the tank. So, (1/12) + (1/X) = 1/6 X = 12 hours

Multiple choice

A pipe can fill a cistern in 8 hours. Due to a leak at its bottom, it is filled in 9 hours. When the cistern is full, in how much time will it be emptied by the leakage?

  1. 72 hours

  2. 17 hours

  3. 31.5 hours

  4. 64 hours

  5. 36 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Part of the capacity of the cistern emptied by leakage in 1 hour = (1/8 - 1/9) = (9 - 8)/(8 * 9) = 1/72

Therefore, the leakage will take 72 hours to empty the cistern. This is answer correct.

Multiple choice

A reservoir can be filled by 4 pipes in 30, 40, 60 and 120 hours, respectively. The first was opened at 6 am, second was opened at 7 am, third was opened at 8 am and fourth was opened at 9 am. At what time will the reservoir be completely full?

  1. 4 pm

  2. 7 pm

  3. 5 pm

  4. 1:30 pm

  5. 7 am
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the time taken after 6 am be t hours.
Therefore, (t/30) + ((t - 1)/40) + ((t - 2)/60) + ((t - 3)/120) = 1                  4t + 3(t - 1) + 2(t - 2) + t - 3 = 120                                           t = 13 hours Therefore, the reservoir will be filled at 7 pm.  It is the correct answer.

Multiple choice

A barrel is full of water. All the water in the barrel is put in equal quantities into three buckets of different sizes. When this operation is completed, it is noted that the first bucket is half full, the second is two-thirds full, while the third is three-quarters full.

If the capacity (in gallons) of the barrel and each of the buckets is a whole number, which of the following options can be the minimum capacity of the barrel?

  1. 6 gallons

  2. 12 gallons

  3. 15 gallons

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

Option 1  – 6 gallons Three buckets contain 6/3 = 2 gallons each The capacity of the three buckets will be: 1st bucket = 2 x 2 = 4 gallons, 2nd bucket = 3/2 x 2 gallons = 3 gallons, 3rd bucket = 4/3 x 2 gallons = 8/3 gallons (False) The capacity of the buckets should be in whole numbers. Option 2 – 12 gallons Three buckets contain 12/3 = 4 gallons each 1st bucket = 4 x 2 = 8 gallons, 2nd bucket = 3/2 x 4 = 6 gallons, 3rd bucket = 4/3 x 4 = 16/3 gallons (False) Option 3 – 15 gallons Three buckets contain 15/3 = 5 gallons each 1st bucket = 5 x 2 = 10 gallons, 2nd bucket = 3/2 x 5 = 15/2 gallons (False) Option 4 – 18 gallons Three buckets contain 18/3 = 6 gallons each 1st bucket = 6 x 2 = 12 gallons, 2nd bucket = 3/2 x 6 = 9 gallons, 3rd bucket = 4/3 x 6 = 8 gallons All conditions are satisfied by option 4. 

Multiple choice

A cistern is supported by two pipes. One of them can fill it in 10 minutes whereas the other can empty it in 12 minutes. The cistern is empty & both the pipes are opened at the same time. When will the cistern be full?

  1. 1 hour 10 minutes

  2. 1 hour 12 minutes

  3. 1 hour 8 minutes

  4. 1 hour

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

(Part of the cistern filled in one minute == 1/10 - 1/12 = 6 - 5/60 = 1/60 Therefore, the cistern is full in 60 minutes or in an hour)

Multiple choice

Two pipes A & B can fill a tank in 24 min. & 32 min. respectively . If both the pipe are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min?

  1. 8 minutes

  2. 2 minutes

  3. 9 minutes

  4. 3 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B be closed after x minutes . Then Part filled by ( A + B ) in x minute + part filled by A in ( 18 - x ) minute = 1 x( 1/24 + 1/32)  + ( 18 - x ) ´ 1/24 = 1 7x/96 + ( 18 - x ) /24 = 1 7x + 4( 18 - x ) = 96 x = 8