$A$ can finish a work in $18$ days and $B$ can do the same work in $15$ days. $B$ worked for $10$ days and left the job. In how many days can $A$ alone finish the remaining work?

$A,$ $B,$ and $C$ can do a work separately in $16,$ $32,$ and $48$ days respectively. They started the work together,but $B$ left $8$ days before and $C$ left $6$ days before the completion of the work. In what time is the work finished? (in days)

$A$ certain sum of money is sufficient to pay wages for $21$ days of $X$ or $28$ days of $Y$. The money is sufficient to pay the wages of both for ........ days.

The work done by a woman in $8\, \text{hours}$ is equal to the work done by a man in $6\, \text{hours}$ and by a boy in $12\, \text{hours}$. If working $6\, \text{hours per day}$,$9$ men can complete a work in $6\, \text{days}$,then in how many $\text{days}$ can $12$ men,$12$ women,and $12$ boys together finish the same work working $8\, \text{hours per day}$?

$6$ men or $12$ women can do a piece of work in $20$ days. In how many days can $8$ men and $16$ women do twice as big as this work?

$A$ can do a piece of work in $30$ days,$B$ in $50$ days,and $C$ in $40$ days. If $A$ is assisted by $B$ on one day and by $C$ on the next day alternately,the work will be completed in (in days):