While working $7$ hours a day,$A$ alone can complete a piece of work in $6$ days and $B$ alone in $8$ days. In what time would they complete it together,working $8$ hours a day? (in days)

$A$ 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?

Three men,four women and six children can complete a work in $7$ days. $A$ woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in $7$ days?

If $10$ men can do a piece of work in $12$ days,the time taken by $12$ men to do the same piece of work will be (in days).

$A$ and $B$ can do a piece of work in $8$ days,$B$ and $C$ can do the same work in $12$ days,and $A, B,$ and $C$ together complete it in $6$ days. The number of days required to finish the work by $A$ and $C$ together is:

$A$ 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?