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Pipes and Cisterns Inverted Cone Problem

XAT 2015 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

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Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%50\%. Which of the following options would be possible?

  1. A.

    Pipe A was open for 19 hours.

  2. B.

    Pipe A was open for 19 hours 30 minutes.

  3. C.

    Pipe B was open for 19 hours 30 minutes.

  4. D.

    Pipe C was open for 19 hours 50 minutes.

  5. E.

    The situation is not possible.

Answer

C

Explanation

When height of cone comes down to 50%50\%, volume remaining =(1/2)3=1/8= (1/2)^3 = 1/8 of total volume. Volume removed =7/8= 7/8 of total capacity. Let total capacity =24= 24 liters. Volume to be removed =78×24=21= \frac{7}{8} \times 24 = 21 liters. Rates: A=+3 l/hA = +3\text{ l/h}, B=+2 l/hB = +2\text{ l/h}, C=−6 l/hC = -6\text{ l/h}. Net rate when all 3 open =3+2−6=−1 l/h= 3 + 2 - 6 = -1\text{ l/h}. In 19 hours, 1919 liters removed. To remove total 21 liters, Pipe B staying open for 19 hours 30 minutes satisfies the total drain required.

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