$P, Q, R$ 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:

The work done by a woman in $8\, \text{hours}$ is equal to the work done by a man in $6\, \text{hours}$ and by a boy in $12\, \text{hours}$. If working $6\, \text{hours per day}$,$9$ men can complete a work in $6\, \text{days}$,then in how many $\text{days}$ can $12$ men,$12$ women,and $12$ boys together finish the same work working $8\, \text{hours per day}$?

$A$ is thrice as good a workman as $B$,therefore,$A$ is able to finish a piece of work in $60 \, days$ less than $B$. The time (in $days$) in which they can do it working together is

$A$ 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?

$A$ and $B$ can complete a piece of work in $18$ days; $B$ and $C$ in $24$ days; $C$ and $A$ in $36$ days. $A$ alone can complete the work in (in days):

$A$ daily wage earner gets a daily wage at the rate of $Rs. 150$ per day,subject to the condition that he will have to pay a penalty at the rate of $Rs. 25$ per day for the days he is absent. At the end of $60$ days,he receives an amount of $Rs. 7,600$. The number of days he worked is: