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$\text{A}$ can do a piece of work in $24$ days,  $\text{B}$ can do the same work in $30$ days and  $\text{C}$ in $40$ days.  $\text{A}$ and  $\text{C}$ worked for $4$ days and handed it to  $\text{B. B}$ worked for some days and handed it again to $\text{A}$ and  $\text{C 6}$ days before completing the work. For how many days did  $\text{B}$ works ?

1. $10$ days
2. $8$ days
3. $6$ days
4. $5$ days

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