$2$ 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?

$A, B$ and $C$ can do a job in $6$ days,$12$ days and $15$ days,respectively. After $\frac{1}{8}$ of the work is completed,$C$ leaves the job. The rest of the work is done by $A$ and $B$ together. The total time taken to finish the work is (in days):

Ajay and Sunil together can complete a piece of work in $10$ days,Sunil and Sanjay in $15$ days,and Sanjay and Ajay in $20$ days. They worked together for $6$ days,and then Ajay leaves. Sunil and Sanjay worked together for $4$ more days,and Sunil leaves. How long will Sanjay take to complete the remaining work? (in days)

$250$ 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:

$A$ labourer can do a job in $36 \text{ hours}$. After $9 \text{ hours}$,he takes a break. What fraction of the job is yet to be done?

$60$ men could complete a work in $250$ days. They worked together for $200$ days. After that,the work had to be stopped for $10$ days due to bad weather. How many more men should be engaged to complete the work on time?