$A$ man is twice as fast as a woman and a woman is twice as fast as a boy in doing a work. If all of them, a man, a woman and a boy, can finish the work in $7$ days, in how many days will a boy do it alone?

$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

$A$ 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):

$A$'s $2$ days work is equal to $B$'s $3$ days work. If $A$ can complete the work in $8$ days,then to complete the work $B$ will take (in days):

$A$ and $B$ can do a piece of work in $12$ days, $B$ and $C$ in $8$ days, and $C$ and $A$ in $6$ days. How long would $B$ take to do the same work alone? (in days)

$A$ and $B$,working together,can complete a piece of work in $12$ days. $B$ and $C$ working together can complete the same piece of work in $16$ days. $A$ worked at it for $5$ days and $B$ worked at it for $7$ days. $C$ finished the remaining work in $13$ days. How many days would $C$ alone take to complete it?