$A$ can do a work in $12 \, days$. When he had worked for $3 \, days$,$B$ joined him. If they complete the work in $3$ more $days$,in how many $days$ can $B$ alone finish the work?

$8$ children and $12$ men complete a certain piece of work in $9$ days. If each child takes twice the time taken by a man to finish the work,in how many days will $12$ men finish the same work?

If $5$ men and $3$ boys can reap $23 \text{ hectares}$ in $4 \text{ days}$ and if $3$ men and $2$ boys can reap $7 \text{ hectares}$ in $2 \text{ days}$,how many boys must assist $7$ men in order that they may reap $45 \text{ hectares}$ in $6 \text{ days}$?

$A$ and $B$ working separately can do a piece of work in $9$ and $15 \, \text{days}$ respectively. If they work on alternate days beginning with $A$,then the work will be completed in how many days?

$A$ can complete a piece of work in $40$ days. He starts working,but having some other engagements,he leaves after $5$ days. Thereafter,$B$ completes the remaining work in $21$ days. How many days would $A$ and $B$ take to complete this work working together?

Working $7\, \text{hours}$ daily,$24$ men can complete a piece of work in $27$ $\text{days}$. In how many $\text{days}$ would $14$ men complete the same piece of work working $9\, \text{hours}$ daily?