$A$ daily-wage labourer was engaged for a certain number of days for $Rs. 5,750$ but being absent on some days he was paid only $Rs. 5,000$. What was his maximum possible daily wage? (in $Rs.$)

$10$ men can complete a piece of work in $15$ days and $15$ women can complete the same work in $12$ days. If all the $10$ men and $15$ women work together,in how many days will the work be completed?

If $10$ persons can do a job in $20$ days,then $20$ persons with twice the efficiency can do the same job in (in days)

$A$ and $B$ together can complete a work in $10$ days. They started together,but $A$ left after $2$ days and the remaining work was completed by $B$ in $12$ days. In how many days can $A$ complete the entire work while working alone?

Kim can do a work in $3 \, \text{days}$ while David can do the same work in $2 \, \text{days}$. Both of them finish the work together and get $Rs. 150$. What is the share of Kim? (in $Rs.$)

$A$ and $B$ together can complete a task in $20$ days. $B$ and $C$ together can complete the same task in $30$ days. $A$ and $C$ together can complete the same task in $40$ days. What is the ratio of the number of days taken by $A$ when completing the same task alone to the number of days taken by $C$ when completing the same task alone?