$4$ men or $6$ women or $10$ children can paint a house in $5$ days. The painting is given to a couple (a man and a woman) and their $5$ sons. They finish the job in (in days):

$A$ can do a work in $20 \, days$ and $B$ in $40 \, days$. If they work on it together for $5 \, days$,then the fraction of the work that is left is:

Nikita,Nishita,and Kavita can complete a work in $2 \frac{2}{3}$ days. If Nishita and Kavita can complete it in $4$ days,and Nishita alone can do it in $6$ days,then in how many days can Nikita and Nishita complete the work?

$P, Q, R$ 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:

Bansal,Gupta,and Singhal together can complete a work in $4 \, \text{days}$. If Bansal and Gupta together can complete the work in $4 \frac{4}{5} \, \text{days}$,and Gupta and Singhal together can do it in $8 \, \text{days}$,then Gupta alone can complete the work in (in $\text{days}$):

$P, Q$ and $R$ undertake to do a work for $Rs. 707$. $P$ and $Q$ together do $\frac{5}{7}$ of the work and the rest is done by $R$ alone. How much should $R$ get? (in $Rs.$)