Rohan and Mohit can build a wall in $8 \, days$,Mohit and Vikas can build the same wall in $10 \, days$,and Vikas and Rohan can build the same in $12 \, days$. In how many days can all three complete the same wall while working together?

$P$ and $Q$ complete a certain work in $30 \, days$,$Q$ and $R$ in $40 \, days$,while $R$ and $P$ in $60 \, days$. How long will they take to finish it together? (in $days$)

If $12$ men and $16$ boys can do a piece of work in $5 \, \text{days}$,and $13$ men and $24$ boys can do it in $4 \, \text{days}$,then the ratio of the daily work done by a man to that of a boy 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?

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)

$A$ daily-wage labourer was engaged for a certain number of days for $Rs. 5,750$ but being absent on some days he was paid only $Rs. 5,000$. What was his maximum possible daily wage? (in $Rs.$)