$A$ and $B$ can do a job in $6$ and $12$ days,respectively. They began the work together,but $A$ leaves after $3$ days. Then,the total number of days needed for the completion of the work is:

If $A$ and $B$ together can complete a piece of work in $15$ days and $B$ alone in $20$ days,in how many days can $A$ alone complete the work?

$A$ does $\frac{4}{5}$ of a work in $20 \, \text{days}$. He then calls in $B$ and they together finish the remaining work in $3 \, \text{days}$. How long would $B$ alone take to do the whole work? (in $\text{days}$)

If $A$ works alone,he would take $4$ days more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone,he would take $16$ days more to complete the job than if $A$ and $B$ work together. How many days would they take to complete the work if both of them worked together?

$A$ and $B$ can do a work in $8$ days,$B$ and $C$ can do the same work in $12$ days. $A, B$ and $C$ together can finish it in $6$ days. $A$ and $C$ together will do it in (in days):

$A$ man,a woman,and a boy can complete a job in $3, 4,$ and $12$ days respectively. How many boys must assist $1$ man and $1$ woman to complete the job in $\frac{1}{4}$ of a day?