$A$ and $B$ can separately do a piece of work in $6 \, \text{days}$ and $12 \, \text{days}$ respectively. How long will they together take to do the work? (in $\text{days}$)

$A$ and $B$ can do a piece of work in $20$ days and $12$ days,respectively. $A$ started the work alone and then after $4$ days $B$ joined him until the completion of the work. How long did the work last? (in days)

Twenty-four men can complete a work in sixteen $days$. Thirty-two women can complete the same work in twenty-four $days$. Sixteen men and sixteen women started working and worked for twelve $days$. How many more men are to be added to complete the remaining work in $2$ $days$?

$A, B$ and $C$ together earn $Rs. 2700$ in $18$ days. $A$ and $C$ together earn $Rs. 940$ in $10$ days. $B$ and $C$ together earn $Rs. 1520$ in $20$ days. Find the daily earning of $C$ (in $Rs.$).

$A$ and $B$ can complete a piece of work in $8$ days,$B$ and $C$ can do it in $12$ days,and $C$ and $A$ can do it in $8$ days. In how many days can $A, B,$ and $C$ together complete the 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):