$A$ can do a piece of work in $30 \text{ days}$ while $B$ can do it in $40 \text{ days}$. $A$ and $B$ working together can do it in (in $\text{days}$)

$A$ can do a certain work in $12$ days. $B$ is $60\%$ more efficient than $A$. How many days will $B$ and $A$ together take to do the same job?

$A$ 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)

$A$ can do a work in $10 \text{ days}$ and $B$ in $20 \text{ days}$. If they work together on it for $5 \text{ days}$,then the fraction of the work that is left is:

$A$ alone can do a piece of work in $6$ days and $B$ alone in $8$ days. $A$ and $B$ undertook to do it for $Rs. 3200$. With the help of $C$,they completed the work in $3$ days. How much is to be paid to $C$ (in $Rs.$)?

Five men and $2$ boys,working together,can complete four times as much work per hour as a man and a boy working together. The ratio of the work completed by a man and a boy is: