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)

$A$ work can be completed by $P$ and $Q$ in $12$ days,$Q$ and $R$ in $15$ days,and $R$ and $P$ in $20$ days. In how many days can $P$ alone finish the work?

$A$ 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?

Five men and $2$ boys,working together,can complete four times as much work per hour as a man and a boy working together. The ratio of the work completed by a man and a boy is:

$A$ can do a work in $5 \, \text{days}$ less than the time taken by $B$ to do it. If both of them together take $11 \frac{1}{9} \, \text{days}$, then the time taken by $B$ alone to do the same work (in $\text{days}$) 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?