Raj and Ram working together can do a piece of work in $10 \text{ days}$. Raj alone can do it in $12 \text{ days}$. In how many days will Ram alone do the work?

$15$ men take $20$ days to complete a job working $8$ hours a day. The number of hours a day $20$ men should work to complete the same job in $12$ days is:

Sixteen men can complete a work in $15$ days,$24$ children can do the same work in $20$ days. In how many days will $8$ men and $8$ children complete the same work?

$A$ can do a job in $6 \, days$ and $A$ and $B$ can do it together in $2 \, days.$ How many $days$ will be taken by $B$ to do the job alone?

Hemant decided to build a farmhouse in $40$ days. He employed $100$ men in the beginning and $100$ more after $35$ days and completed the construction in the stipulated time. If he had not employed the additional men,how many days behind schedule would it have been finished? (in days)

$12$ men can complete a piece of work in $4$ days,while $15$ women can complete the same work in $4$ days. $6$ men start working on the job and after working for $2$ days,all of them stopped working. How many women should be put on the job to complete the remaining work,if it is to be completed in $3$ days?