$A$ 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.

$4$ mat-weavers can weave $4$ mats in $4$ days. At the same rate,how many mats would be woven by $8$ mat-weavers in $8$ days?

$12$ men and $16$ boys can do a piece of work in $5$ days. $13$ men and $24$ boys can do it in $4$ days. Then,the ratio of the daily work done by a man to that of a boy is:

Sita takes twice as much time as Gita to complete a work and Rita does it in the same time as Sita and Gita together. If all three working together can finish the work in $6$ days,then the time taken by each of them to finish the work is (in days):

$A$ and $B$ together can complete a piece of work in $12$ days and $B$ and $C$ together in $15$ days. If $A$ is twice as good a workman as $C$,then in how many days will $B$ alone complete the same work?

$X$ and $Y$ can do a piece of work in $20$ days and $12$ days respectively. $X$ started the work alone and then after $4$ days $Y$ joined him until the completion of the work. How long did the work last? (in days)