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}

  • 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}

  • 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}