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Pipes and Cisterns Closing Time

CMAT 2021 · Quantitative Techniques & Data Interpretation · Medium · Pipes and Cisterns

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Pipe X can fill a tank in 12 hours and pipe Y can empty the tank in 18 hours. Both pipes are opened at 8 am and after some time Y is closed, and the tank is full at 10 pm on the same day. At what time was pipe Y closed?

  1. A.

    1 pm

  2. B.

    10 am

  3. C.

    11 am

  4. D.

    12 noon

Answer

C

Explanation

Let total capacity of the tank = LCM(12,18)=36\text{LCM}(12, 18) = 36 units. Efficiency of X = +3 units/hr, efficiency of Y = -2 units/hr. From 8 am to 10 pm is 14 hours. Pipe X was open for all 14 hours, filling 14×3=4214 \times 3 = 42 units. Since capacity is 36 units, Y must have emptied 42−36=642 - 36 = 6 units. Time Y was open = 62=3\frac{6}{2} = 3 hours. So pipe Y was closed 3 hours after 8 am, which is at 11 am.

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