$A$ 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 separately do a piece of work in $6 \, \text{days}$ and $12 \, \text{days}$ respectively. How long will they together take to do the work? (in $\text{days}$)

Working efficiencies of $A$ and $B$ for completing a piece of work are in the ratio $3: 4$. The number of days taken by them to complete the work will be in the ratio:

$A$ does a work in $10$ $days$ and $B$ does the same work in $15$ $days$. In how many $days$ will they together do the same work?

$A$ can do a piece of work in $120$ days and $B$ can do it in $150$ days. They work together for $20$ days. Then $B$ leaves and $A$ alone continues the work. After $12$ days,$C$ joins $A$ and the work is completed in $48$ days more. In how many days can $C$ do it if he works alone?

$A$ and $B$ working separately can do a piece of work in $9$ and $12$ days,respectively. If they work for a day alternatively with $A$ beginning,the work would be completed in (in days):