Practice Test Discussion

Q)

Three taps A, B and C can fill an empty cistern in 10 min. The tap A alone can fill it in 30 min and the tap B alone in 40 min. How long will tap C alone take to fill it?

[SSC CGL 2010]


  • Explanation

    According to the above given formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is xyzyz+xz-xy hours.

    According to the question x+y+z=10

    So,

     10=30×40×z(30×40)+(40×z)+(z×30)10=1200z1200+30z+40z10=1200z1200+70z

    Upon cross multiplication,

    101200+70z=1200z12000+700z=1200z12000=1200z-700z12000=500zz=12000500z=24 minutes

    Hence, the tank will be emptied in 24 minutes.

    Hence option B is correct.

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    Pipes and cisterns

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