$4$ 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?

$A$ can finish a work in $18$ days and $B$ can do the same work in half the time taken by $A$. Then,working together,what part of the same work can they finish in a day?

$A$ alone can complete a work in $16$ days and $B$ alone in $12$ days. Starting with $A$,they work on alternate days. The total work will be completed in (in days):

$12$ men complete a work in $9$ days. After they have worked for $6$ days,$6$ more men join them. How many days will they take to complete the remaining work?

$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is:

$A$ and $B$ together can complete a work in $12$ days. $A$ alone can complete it in $20$ days. If $B$ does the work only for half a day daily,then in how many days will $A$ and $B$ together complete the work?