Two pipes $A$ and $B$ can fill a cistern in $15$ and $20$ $min$,respectively. Both the pipes are opened together,but after $2$ $min$,pipe $A$ is turned off. What is the total time (in $minutes$) required to fill the tank?

  • A
    $\frac{46}{3} \text{ min}$
  • B
    $\frac{52}{3} \text{ min}$
  • C
    $\frac{58}{3} \text{ min}$
  • D
    $\frac{41}{3} \text{ min}$

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