Pipes and Cisterns Problems and Solutions

• 1. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

  1. 6 min to empty
  2. 7 min to full
  3. 6 min to full
  4. 7 min to empty

  Answer :

  Option A

  Explanation:

  There are two important points to learn in this type of question,
  First, if both will open then tank will be empty first.
  
  Second most important thing is,
  If we are calculating filling of tank then we will subtract as (filling-empting)
  
  If we are calculating empting of thank then we will subtract as (empting-filling)
  
  So lets come on the question now,
  
  Part to emptied 2/5
  
  Part emptied in 1 minute =
  \begin{aligned}
  \frac{1}{6} - \frac{1}{10} \\
  = \frac{1}{15} \\
  => \frac{1}{15}:\frac{2}{5}::1:x \\
  => \frac{2}{5}*15 = 6 mins
  
  \end{aligned}

• 2. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?

  1. 8 min 15 sec
  2. 7 min 15 sec
  3. 6 min 15 sec
  4. 5 min 15 sec

  Answer :

  Option A

  Explanation:

  Part filled in 3 minutes =
  \begin{aligned}
  3*\left(\frac{1}{12} + \frac{1}{15}\right) \\
  = 3*\frac{9}{60} = \frac{9}{20}\\
  \text{Remaining part }= 1-\frac{9}{20} \\
  = \frac{11}{20} \\
  => \frac{1}{15}:\frac{11}{20}=1:X \\
  => X = \frac{11}{20}*\frac{15}{1} \\
  => X = 8.25 mins
  \end{aligned}
  
  So it will take further 8 mins 15 seconds to fill the bucket.

• 3. A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?

  1. 20 hours
  2. 19 hours
  3. 90 hours
  4. 80 hours

  Answer :

  Option C

  Explanation:

  Part filled without leak in 1 hour = 1/9
  Part filled with leak in 1 hour = 1/10
  
  Work done by leak in 1 hour \begin{aligned}
  = \frac{1}{9} - \frac{1}{10} \\
  = \frac{1}{90}
  \end{aligned}
  
  We used subtraction as it is getting empty.
  
  So total time to empty the cistern is 90 hours

• 4. Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?

  1. 2.5 hours
  2. 2 hours
  3. 3.5 hours
  4. 3 hours

  Answer :

  Option D

  Explanation:

  Part filled by A in 1 hour = 1/5
  Part filled by B in 1 hour = 1/10
  Part filled by C in 1 hour = 1/30
  
  Part filled by (A+B+C) in 1 hour =
  \begin{aligned}
  \frac{1}{5}+\frac{1}{10}+\frac{1}{30} \\
  = \frac{1}{3} \\
  \end{aligned}
  
  So all pipes will fill the tank in 3 hours.

• 5. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled ?

  1. 7 hours
  2. 7.1 hours
  3. 7.2 hours
  4. 7.3 hours
  5. 61%
  6. 47%
  7. 59%
  8. 69%

  Answer :

  Option

  Explanation:

  When we have question like one is filling the tank and other is empting it, then we subtraction as,
  
  Filled in 1 hour = 1/4
  Empties in 1 hour = 1/9
  
  Net filled in 1 hour = 1/4 - 1/9
  = 5/36
  
  So cistern will be filled in 36/5 hours i.e. 7.2 hours

• 6. 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

  1. 15 bukets
  2. 17 bukets
  3. 18 bukets
  4. 19 bukets

  Answer :

  Option C

  Explanation:

  Capacity of the tank = (12*13.5) litres
  = 162 litres
  Capacity of each bucket = 9 litres.
  So we can get answer by dividing total capacity of tank by total capacity of bucket.
  Number of buckets needed = (162/9) = 18 buckets
  

• 7. A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.
  

  1. 2 hours 30 mins
  2. 2 hours 45 mins
  3. 3 hours 30 mins
  4. 3 hours 45 mins

  Answer :

  Option D

  Explanation:

  Half tank will be filled in 3 hours
  Lets calculate remaining half,
  
  Part filled by the four taps in 1 hour = 4*(1/6) = 2/3
  
  Remaining part after 1/2 filled = 1-1/2 = 1/2
  
  \begin{aligned}
  \frac{2}{3}:\frac{1}{2}::1:X \\
  
  => X = \left( \frac{1}{2}*1*{3}{2} \right) \\
  => X = \frac{3}{4} hrs = 45 \text{ mins} \\
  
  \end{aligned}
  Total time = 3 hours + 45 mins = 3 hours 45 mins