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Pipes and Cisterns Questions Answers

  • 8. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?

    1. 10 hours
    2. 13 hours
    3. 17 hours
    4. 21 hours
    Answer And Explanation

    Answer: Option D

    Explanation:

    We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as

    Work done for 1 hour without leak = 1/3
    Work done with leak =
    \begin{aligned}
    3\frac{1}{2} = \frac{7}{2} \\
    \text{Work done with leak in 1 hr= }\frac{2}{7} \\
    \text{Work done by leak in 1 hr }\\
    = \frac{1}{3} - \frac{2}{7} = \frac{1}{21}
    \end{aligned}

    So tank will be empty by the leak in 21 hours.

  • 9. A tank can be filled by a tap in 20 minutes and by another tap in 60 minutes. Both the taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will be completely filled in what time ?

    1. 10 mins
    2. 15 mins
    3. 20 mins
    4. 25 mins
    Answer And Explanation

    Answer: Option C

    Explanation:

    How we can solve this question ?
    First we will calculate the work done for 10 mins, then we will get the remaining work, then we will find answer with one tap work, As

    Part filled by Tap A in 1 min = 1/20
    Part filled by Tap B in 1 min = 1/60

    (A+B)'s 10 mins work =
    \begin{aligned}
    10*\left(\frac{1}{20}+\frac{1}{60}\right) \\
    = 10*\frac{4}{60} = \frac{2}{3} \\
    \text{Remaining work = } 1-\frac{2}{3} \\
    = \frac{1}{3} \\

    \text{METHOD 1} \\
    => \frac{1}{60}:\frac{1}{3}=1:X \\
    => X = 20 \\

    \text{METHOD 2} \\

    1/60 \text{ part filled by B in} = 1 min \\
    1/3 \text{ part will be filled in} \\
    = \frac{\frac{1}{3}}{\frac{1}{60}} \\
    = \frac{60}{3} = 20
    \end{aligned}

  • 10. 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 And Explanation

    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

  • 11. 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 And Explanation

    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.

  • 12. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by the first pipe to fill the tank ?

    1. 10 hours
    2. 15 hours
    3. 17 hours
    4. 18 hours
    Answer And Explanation

    Answer: Option B

    Explanation:

    Suppose, first pipe alone takes x hours to fill the tank .

    Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.

    As per question, we get
    \begin{aligned}
    \frac{1}{x} + \frac{1}{x-5} = \frac{1}{x-9} \\
    => \frac{x-5+x}{x(x-5)} = \frac{1}{x-9}\\
    => (2x - 5)(x - 9) = x(x - 5)\\
    => x^2 - 18x + 45 = 0
    \end{aligned}

    After solving this euation, we get
    (x-15)(x+3) = 0,
    As value can not be negative, so x = 15

  • 13. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in

    1. 144 mins
    2. 140 mins
    3. 136 mins
    4. 132 minw
    Answer And Explanation

    Answer: Option A

    Explanation:

    Let the slower pipe alone fill the tank in x minutes
    then faster will fill in x/3 minutes.

    Part filled by slower pipe in 1 minute = 1/x
    Part filled by faster pipe in 1 minute = 3/x

    Part filled by both in 1 minute = \begin{aligned}
    \frac{1}{x} + \frac{3}{x}= \frac{1}{36} \\
    => \frac{4}{x} = \frac{1}{36} \\
    x = 36*4 = 144 mins
    \end{aligned}

  • 14. 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 And Explanation

    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