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Quiz: Pipes and Cisterns

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Number of Questions: 14

Question: 6 -

25 outlets working 6 hours a day, can empty a reservoir in 10 days. If only 15 outlets are operational and work for 4 hours a day, in how many days the reservoir can be emptied?

Options:

  1. 25 days

  2. 22 days

  3. 18 days

  4. 20 days

    5. Answer:

    25 days
    Solution:

    Apply formula used in work and time problems; M1D1T1W2 = M2D2T2W1

    M1= 25 outlets, D1=10 days, T1= 6 hours/day, W2 = to fill the reservoir

    M2= 15 outlets, D2=? T2 = 4 hours/day, W1= to fill the reservoir

    W1=W2

    So we have; M1D1T1= M2D2T2

    25*10*6=15*D2*4

    1500 = 60 * D2

    Apti Pipes and cisterns52

Question: 7 -

Two pipes working together can fill a fish tank in 12 minutes. If one pipe fills the fish tank 10 minutes faster than the second pipe, in what time the second pipe alone can fill the fish tank?

Options:

  1. 35

  2. 30

  3. 25

  4. 20

    5. Answer:

    30
    Solution:

    Let the first pipe fill the reservoir in X minutes

    So, the second pipe will fill the reservoir in (X+10) minutes

    As per question;

    Apti Pipes and cisterns51

    12X +120 + 12X = X2 + 10X

    X2 +10X 24X -120 = 0

    X2 14X -120 =0

    X2 - 20X+6X 120=0

    X(X-20) +6(X-20) =0

    (X+6) (X-20) = 0

    X = 20

    ∴Second pipe will fill the reservoir in 20 + 10= 30 minutes

Question: 8 -

Pipe A can fill a tank in 12 minutes whereas pipe A along with pipe B can fill the same tank in 8 minutes. In what time pipe B alone can fill the tank?

Options:

  1. 22

  2. 20

  3. 25

  4. 24

    5. Answer:

    24
    Solution:

    Part of the tank filled by pipe A in one minute=Apti Pipes and cisterns53

    Part of the tank filled by A+B in one minute =Apti Pipes and cisterns54

    Part of the tank filled by B alone =Apti Pipes and cisterns55

    Apti Pipes and cisterns56

    ∴ Pipe B will fill the whole tank in 24 minutes.

    Solution 2:

    Apti Pipes and cisterns57

    X= 12 minutes

    Y=?

    As per question;

    Apti Pipes and cisterns58

    12Y= 8Y+96

    4Y= 96

    Y = 24 minutes

Question: 9 -

A cistern can be filled by an inlet in 6 hours and can be emptied by an outlet in 8 hours. If the inlet and outlet are opened together, in what time the cistern can be filled?

Options:

  1. 24 hours

  2. 20 hours

  3. 18 hours

  4. 26 hours

    5. Answer:

    24 hours
    Solution:

    Part of the tank filled by the inlet in one hour = Apti Pipes and Cisterns
    Part of the tank emptied by the outlet in one hour = Apti Pipes and Cisterns
    Net part of the tank filled in one hour = Apti Pipes and Cisterns - Apti Pipes and Cisterns

    Apti Pipes and Cisterns

    Apti Pipes and Cisterns part of the tank is filled in one hour

    ∴ The whole tank will be filled in 24 hours.

    Solution 2:
    Apply formula; =Apti Pipes and Cisterns

    X = 6 hours

    Y = 8 hours
    ∴ Required time = Apti Pipes and Cisterns = 24 hours

Question: 10 -

20 buckets can fill a tank when the capacity of each bucket is 12 liters. If the capacity of each bucket is 10 liters, find the number of buckets required to fill the tank.

Options:

  1. 24 buckets

  2. 34 buckets

  3. 27 buckets

  4. 30 buckets

    5. Answer:

    24 buckets
    Solution:

    Capacity of each bucket = 12 liters

    20 buckets can fill the tank. So, capacity of tank = 20 * 12= 240 liters

    New capacity of bucket = 10 liters

    So, 10 liters can be poured into the tank by one bucket

    Apti Pipes and cisterns50