$P$ and $Q$ working together can complete a certain work in $6 \, \text{days}$. $Q$ alone can do it in $8 \, \text{days}$. In how many $\text{days}$ could $P$ alone finish the same work?

Two men undertake a piece of work for $Rs. 600$. Individually,they can complete the work in $6$ days and $8$ days,respectively. With the assistance of a boy,they completed the work in $3$ days. The boy's share should be (in $Rs.$)

$A$ and $B$ can do a work in $12$ days,$B$ and $C$ in $15$ days,and $C$ and $A$ in $20$ days. If $A, B,$ and $C$ work together,they will complete the work in (in days):

$A$ 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:

$2$ men and $3$ women together or $4$ men together can complete a piece of work in $20$ days. $3$ men and $3$ women will complete the same work in (in days):

$6$ men or $12$ women can do a piece of work in $20$ days. In how many days can $8$ men and $16$ women do twice as big as this work?