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    Question

    The efficiency of pipe R is 60% more than the efficiency

    of pipe S. Pipe Q alone can fill 30% of the empty tank in 6 hours. Pipe R alone can fill an empty tank completely in (y-5) hours. The ratio between the efficiencies of pipe P and R is 5:6 respectively. Pipe P and Q together can fill 25% of the empty tank in 3 hours. Find out the time taken by pipe S alone to fill 55% of the tank and the value of ‘y’.
    A 28 hours, 40 Correct Answer Incorrect Answer
    B 22 hours, 30 Correct Answer Incorrect Answer
    C 36 hours, 30 Correct Answer Incorrect Answer
    D 20 hours, 40 Correct Answer Incorrect Answer

    Solution

    Let’s assume the capacity of the tank is 600 units.

    Pipe Q alone can fill 30% of the empty tank in 6 hours.

    Time taken by Pipe Q alone to fill the tank completely = (6/30)x100

    = 20 hours

    Efficiency of pipe Q = 600/20 = 30 units/hour    Eq.(i)

    Pipe P and Q together can fill 25% of the empty tank in 3 hours.

    Time taken by Pipe P and Q together to fill the tank completely = (3/25)x100

    = 12 hours

    Efficiency of pipe P and Q together = 600/12 = 50 units/hour    Eq.(ii)

    Efficiency of pipe P = Eq.(ii)-Eq.(i)

    = 50-30

    = 20 units/hour

    The ratio between the efficiencies of pipe P and R is 5:6 respectively.

    Efficiency of pipe R = (20/5)x6

    = 24 units/hour

    The efficiency of pipe R is 60% more than the efficiency of pipe S.

    24 = (100+60)% of the efficiency of pipe S

    24 = 160% of the efficiency of pipe S

    efficiency of pipe S = 24/1.6

     = 240/16

    = 15 units/hour

    Pipe R alone can fill an empty tank completely in (y-5) hours.

    (Efficiency of pipe R) x (time taken by pipe R to fill an empty tank completely) = total capacity of the tank

    24 x (y-5) = 600

    4 x (y-5) = 100

    (y-5) = 25

    y = 25+5

    y = 30

    Time taken by pipe S alone to fill 55% of the tank = 55% of (total capacity of the tank)/(efficiency of pipe S)

    = 55% of (600)/(15)

    = 55% of 40

    = 22 hours

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