$A$ can do a certain work in the same time in which $B$ and $C$ together can do it. If $A$ and $B$ together could do it in $10 \text{ days}$ and $C$ alone in $50 \text{ days}$,then $B$ alone could do it in (in $\text{days}$):

$A$ can do a piece of work in $15 \text{ days}$. With the help of $A$,$B$ can do it in $6 \frac{2}{3} \text{ days}$. $B$ can do it alone in (in $\text{days}$)

$A$ and $B$ together can complete a work in $12$ days. $A$ alone can complete it in $20$ days. If $B$ does the work only for half a day daily,then in how many days will $A$ and $B$ together complete the work?

$A$ is $20\%$ more efficient than $B$. If $B$ alone can complete a piece of work in $12$ days,then $A$ alone can complete the same work in how many days?

$2$ men and $4$ boys can do a piece of work in $10$ days,while $4$ men and $5$ boys can do it in $6$ days. Men and boys are paid wages according to their output. If the daily wage of a man is $Rs. 40$,then the ratio of daily wages of a man and a boy will be

$A$ can complete a piece of work in $40$ days. He starts working,but having some other engagements,he leaves after $5$ days. Thereafter,$B$ completes the remaining work in $21$ days. How many days would $A$ and $B$ take to complete this work working together?