Time and Work and Wages question bank (Quantitative Aptitude)

$A$ and $B$ can do a piece of work in $20$ days and $12$ days,respectively. $A$ started the work alone and then after $4$ days $B$ joined him until the completion of the work. How long did the work last? (in days)

$A$ and $B$ can do a work in $12$ days. $B$ and $C$ can do the same work in $15$ days. $C$ and $A$ can do the same work in $20$ days. How much time will $A, B,$ and $C$ take to complete the same work together (in days)?