$A,$ $B,$ and $C$ can do a work separately in $16,$ $32,$ and $48$ days respectively. They started the work together,but $B$ left $8$ days before and $C$ left $6$ days before the completion of the work. In what time is the work finished? (in days)

$A$ can finish a work in $24 \, days$,$B$ in $9 \, days$,and $C$ in $12 \, days$. $B$ and $C$ start the work but are forced to leave after $3 \, days$. The remaining work was done by $A$ in (in $days$):

$A$ does half as much work as $B$ in $three-fourths$ of the time. If together they take $18$ days to complete a work,how much time shall $B$ take to do it alone? (in days)

$A$ $10\, \text{hectare}$ field is reaped by $2\, \text{men},$ $3\, \text{women},$ and $4\, \text{children}$ together in $10\, \text{days}.$ If the working capabilities of a man, a woman, and a child are in the ratio $5: 4: 2,$ then a $16\, \text{hectare}$ field will be reaped by $6\, \text{men},$ $4\, \text{women},$ and $7\, \text{children}$ in how many days?

$X$ and $Y$ can do a piece of work in $20$ days and $12$ days respectively. $X$ started the work alone and then after $4$ days $Y$ joined him until the completion of the work. How long did the work last? (in days)

$A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They began to do the work together,but $A$ leaves after some days and then $B$ completed the remaining work in $23$ days. The number of days after which $A$ left the work was: