$A, B$ 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)

$10$ men working $6\, \text{h}$ a day can complete a work in $18\, \text{days}$. How many $\text{hours per day}$ must $15$ men work to complete the same work in $12\, \text{days}$?

$P$ 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

$A$ piece of work can be completed by $10$ men and $6$ women in $18$ days. Men work $9$ hours per day while women work $7.5$ hours per day. The per hour efficiency of a woman is $\frac{2}{3}$ of a man's efficiency. In how many days will $10$ men and $9$ women complete the work?

$A$ and $B$ can do a piece of work in $12$ days and $15$ days,respectively. They began to work together,but $A$ left after $4$ days. In how many more days would $B$ alone complete the remaining work?

$A$ works thrice as good as $B$ and is,therefore,able to finish a piece of work in $60 \text{ days}$ less than $B$. Find the time in which they can complete it,working together (in $\text{days}$).