$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?

$250$ men can finish a work in $20 \, \text{days}$ working $5 \, \text{hours}$ a day. To finish the work within $10 \, \text{days}$ working $8 \, \text{hours}$ a day,the minimum number of men required is:

$A$ does $\frac{1}{5}$ of a work in a $week$. $B$ finishes the same in a fortnight. $B$ starts the work and works only for $3$ days. Thereafter,$A$ completes the job. In how many days will $A$ finish the remaining work?

$A$ certain number of men complete a work in $160\, days$. If there were $38\, men$ more, the work could be finished in $20\, days$ less. How many men were originally there?

$A$ can do a work in $20 \, days$ and $B$ in $40 \, days$. If they work on it together for $5 \, days$,then the fraction of the work that is left is:

$A, B$ and $C$ can do a piece of work in $30, 20$ and $10$ days respectively. $A$ is assisted by $B$ on one day and by $C$ on the next day,alternately. How long would the work take to finish? (in days)