If $4$ men or $8$ women can do a piece of work in $15$ days,in how many days can $6$ men and $12$ women do the same piece of work?

$A$ and $B$ can do a job alone in $12 \text{ days}$ and $15 \text{ days}$ respectively. $A$ starts the work and after $6 \text{ days}$,$B$ also joins to finish the work together. For how many days did $B$ actually work on the job?

$A$ can complete a work in $10$ days,$B$ can complete the same work in $20$ days,and $C$ in $40$ days. $A$ starts working on the first day,$B$ works on the second day,and $C$ works on the third day. Again,$A$ works on the fourth day,$B$ on the fifth day,and so on. If they continue working in the same way,in how many days will the work be completed?

$P$ and $Q$ together can do a job in $6$ days. $Q$ and $R$ can finish the same job in $60/7$ days. $P$ started the work and worked for $3$ days. $Q$ and $R$ continued for $6$ days. Then the difference of days in which $R$ and $P$ can complete the job is

Working efficiencies of $A$ and $B$ for completing a piece of work are in the ratio $3: 4$. The number of days taken by them to complete the work will be in the ratio:

$60$ 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?