Pipes and Cisterns Questions Answers

• 15. A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other half.

  1. 15 mins
  2. 20 mins
  3. 25 mins
  4. 30 mins

  Answer And Explanation

  Answer: Option D

  Explanation:

  Let the total time be x mins.
  Part filled in first half means in x/2 = 1/40
  
  Part filled in second half means in x/2 = \begin{aligned}
  \frac{1}{60}+\frac{1}{40} \\
  = \frac{1}{24} \\
  \text{ Total = } \\
  \frac{x}{2}*\frac{1}{40} + \frac{x}{2}*\frac{1}{24} = 1 \\
  
  => \frac{x}{2} \left(\frac{1}{40}+\frac{1}{24} \right) = 1 \\
  => \frac{x}{2}*\frac{1}{15} = 1 \\
  => x = 30 mins
  \end{aligned}

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• 16. Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ?

  1. 3 hours
  2. 5 hours
  3. 7 hours
  4. 10 hours

  Answer And Explanation

  Answer: Option B

  Explanation:

  (A+B)'s 2 hour's work when opened =
  \begin{aligned}
  \frac{1}{6}+\frac{1}{4} = \frac{5}{12} \\
  
  (A+B)'s \text{ 4 hour's work} = \frac{5}{12}*2 \\
  = \frac{5}{6}
  
  \text{Remaining work = } 1-\frac{5}{6} \\
  = \frac{1}{6} \\
  
  \text{Now, its A turn in 5 th hour} \\
  \frac{1}{6} \text{ work will be done by A in 1 hour}\\
  \text{Total time = }4+1 = 5 hours
  \end{aligned}

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• 17. There are two pipes which are functioning simultaneouly to fill a tank in 12 hours, if one pipe fills the tank 10 hours faster than other then how many hours second pipe will take to fill the tank ?

  1. 30 hours
  2. 35 hours
  3. 40 hours
  4. 42 hours

  Answer And Explanation

  Answer: Option A

  Explanation:

  Lets suppose tank got filled by first pipe in X hours,
  So, second pipe will fill the tank in X + 10 hours.
  
  \begin{aligned}
  => \frac{1}{X} + \frac{1}{X} + 10 = \frac{1}{12} \\
  => X = 20
  \end{aligned}

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