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Pipes and Cisterns Questions Answers

  • 1. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?

    1. 10 mins
    2. 12 mins
    3. 15 mins
    4. 20 mins
    Answer And Explanation

    Answer: Option B

    Explanation:

    In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as

    Part filled by A in 1 min = 1/20
    Part filled by B in 1 min = 1/30

    Part filled by (A+B) in 1 min = 1/20 + 1/30
    = 1/12

    So both pipes can fill the tank in 12 mins.

  • 2. 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
    Answer And Explanation

    Answer: Option C

    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

  • 3. 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 And Explanation

    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

  • 4. 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 And Explanation

    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}

  • 5. 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 And Explanation

    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.

  • 6. Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in.

    1. \begin{aligned} 3\frac{9}{5} \end{aligned}
    2. \begin{aligned} 3\frac{9}{17} \end{aligned}
    3. \begin{aligned} 3\frac{7}{5} \end{aligned}
    4. \begin{aligned} 3\frac{7}{17} \end{aligned}
    Answer And Explanation

    Answer: Option B

    Explanation:

    Net part filled in 1 hour =
    \begin{aligned}
    \left(\frac{1}{5}+\frac{1}{6}-\frac{1}{12}\right) \\
    = \frac{17}{60} hrs \\
    = 3\frac{9}{17}
    \end{aligned}

  • 7. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is

    1. 5780 litres
    2. 5770 litres
    3. 5760 litres
    4. 5750 litres
    Answer And Explanation

    Answer: Option C

    Explanation:

    Work done by the inlet in 1 hour =
    \begin{aligned}
    \frac{1}{6}-\frac{1}{8} = \frac{1}{24} \\
    \text{Work done by inlet in 1 min} \\
    = \frac{1}{24}*\frac{1}{60}\\
    = \frac{1}{1440} \\
    => \text{Volume of 1/1440 part = 4 liters} \\

    \end{aligned}

    Volume of whole = (1440 * 4) litres = 5760 litres.