If $10$ men can do a piece of work in $12$ days,the time taken by $12$ men to do the same piece of work will be (in days).

$6$ men can complete a piece of work in $12$ days. $8$ women can complete the same piece of work in $18$ days,whereas $15$ children can complete the piece of work in $10$ days. $4$ men,$12$ women,and $20$ children work together for $2$ days. If only men were to complete the remaining work in $1$ day,how many men would be required?

$2$ 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?

$A$ can do a piece of work in $4 \, days$ and $B$ can do it in $12 \, days.$ In how many $days$ will they finish the work,both working together?

$A$ certain number of men complete a work in $160\, days$. If there were $38\, men$ more, the work could be finished in $20\, days$ less. How many men were originally there?

$A$ can do a piece of work in $30$ days while $B$ can do it in $40$ days. In how many days can $A$ and $B$ working together do it?