$A$ and $B$ together can complete a piece of work in $12$ days and $B$ and $C$ together in $15$ days. If $A$ is twice as good a workman as $C$,then in how many days will $B$ alone complete the same work?

If $A$ and $B$ together can complete a work in $18$ days,$A$ and $C$ together in $12$ days,and $B$ and $C$ together in $9$ days,then $B$ alone can do the work in (in days)

Ramesh takes twice as much time as Mahesh and thrice as much time as Suresh to complete a job. If working together,they can complete the job in $4 \, \text{days}$,then the time taken by each of them separately to complete the work is (in $\text{days}$)

$3$ women and $18$ children together take $2$ days to complete a piece of work. How many days will $9$ children alone take to complete the piece of work,if $6$ women alone can complete the piece of work in $3$ days?

Twenty women can do a work in $16$ days. Sixteen men can complete the same work in $15$ days. What is the ratio between the capacity of a man and a woman?

$A$ certain number of persons can complete a piece of work in $55 \text{ days}$. If there were $6$ persons more,the work could be finished in $11 \text{ days}$ less. How many persons were originally there?