$A$ certain number of men can do a piece of work in $40 \, days$. If there were $45 \, men$ more,the work could have been finished in $25 \, days$. Find the original number of men employed in the work.

$A$ does a work in $10$ $days$ and $B$ does the same work in $15$ $days$. In how many $days$ will they together do the same work?

$8$ men can complete a piece of work in $20$ days. $8$ women can complete the same work in $32$ days. In how many days will $5$ men and $8$ women together complete the same work?

$2$ 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 $Rs.$)

$A$ 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?

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?