$A$ can do a work in $15 \text{ days}$ and $B$ in $20 \text{ days}$. If they work together on it for $4 \text{ days}$,then the fraction of the work that is left is

$2$ men and $3$ women can complete a work in $10$ days,while $4$ men can complete it in $10$ days. In how many days will $3$ men and $3$ women complete the work?

$4$ men and $6$ women together can complete a work in $8$ days,while $3$ men and $7$ women together can complete it in $10$ days. $20$ women working together will complete it in (in days):

$A$ can do a piece of work in $16$ days and $B$ in $24$ days. They take the help of $C$ and all three together finish the work in $6$ days. If the total remuneration for the work is $Rs. 400$,what is the amount (in $Rs.$) each will receive in proportion to the work done?

$4$ men and $6$ women can complete a work in $8$ days,while $3$ men and $7$ women can complete it in $10$ days. In how many days will $10$ women complete it?

One man,$3$ women,and $4$ boys can do a work in $96$ hours,$2$ men and $8$ boys can do it in $80$ hours,and $2$ men and $3$ women can do it in $120$ hours. In how many hours can it be done by $5$ men and $12$ boys? (in hours)