$A$ pipe can fill a cistern in $4$ $min$ and another pipe can fill it in $5$ $min,$ but a third pipe can empty it in $2$ $min.$ The first two pipes are kept open for $2$ $min$ in the beginning and then the third pipe is also opened. Time (in $min$) taken to empty the cistern is?

  • A
    $20$
  • B
    $22$
  • C
    $42$
  • D
    $18$

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