While working $7$ hours a day,$A$ alone can complete a piece of work in $6$ days and $B$ alone in $8$ days. In what time would they complete it together,working $8$ hours a day? (in days)

Working $7\, \text{hours}$ daily,$24$ men can complete a piece of work in $27$ $\text{days}$. In how many $\text{days}$ would $14$ men complete the same piece of work working $9\, \text{hours}$ daily?

$2$ men and $1$ woman can do a piece of work in $14$ days,while $4$ women and $2$ men can do the same work in $8$ days. If a man gets $Rs. 90$ per day,what should be the wages per day of a woman? (in $Rs.$)

$A$ piece of work was to be completed in $40$ days. $A$ number of men employed upon it did only half the work in $24$ days. $16$ more men were then set on,and the work was completed in the specified time. How many men were employed at first?

$6$ 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?

$4$ men and $6$ women complete a work in $8$ days,$2$ men and $9$ women also complete the same work in $8$ days. In how many days will $18$ women complete the work?