$A$ 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.

If $x$ men can do a piece of work in $x$ days,then the number of days in which $y$ men can do the same work is (in days)

Ram can finish a work in $15 \text{ days}$ working $8 \text{ hrs/day}$. Fari can finish it in $6 \frac{2}{3} \text{ days}$ at $9 \text{ hrs/day}$. Find in how many days both can finish it together,if both work $10 \text{ hrs/day}$?

$A$ and $B$ can do a piece of work in $8$ days,$B$ and $C$ can do the same work in $12$ days,and $A, B,$ and $C$ together complete it in $6$ days. The number of days required to finish the work by $A$ and $C$ together is:

$P, Q, R$ are employed to do a work for $Rs. 5750$. $P$ and $Q$ together finished $\frac{19}{23}$ of the work,and $Q$ and $R$ together finished $\frac{8}{23}$ of the work. The wage of $Q$ (in rupees) is:

$A$ alone can complete a work in $18 \, days$ and $B$ alone in $15 \, days.$ $B$ alone worked at it for $10 \, days$ and then left the work. In how many more days will $A$ alone complete the remaining work?