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Pipes and cisterns time to empty

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Time and Work

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Two pipes A and B can fill a cistern in 120 minutes and 150 minutes respectively. There is also an outlet C. If all the three pipes are opened together, the cistern gets filled in 100 minutes. How much time will be taken by C to empty full tank?

  1. A.

    3 h 20 min

  2. B.

    2 h 40 min

  3. C.

    3 h

  4. D.

    3 h 40 min

Answer

A

Explanation

Let capacity = 600 units. Efficiency of A = 600120=5\frac{600}{120} = 5 units/min. Efficiency of B = 600150=4\frac{600}{150} = 4 units/min. Combined efficiency (A+B−C)=600100=6(A + B - C) = \frac{600}{100} = 6 units/min. 5+4−C=6  ⟹  C=35 + 4 - C = 6 \implies C = 3 units/min. Time taken by C = 6003=200 minutes=3 h 20 min\frac{600}{3} = 200\text{ minutes} = 3\text{ h } 20\text{ min}.

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