$A$ is thrice as good a workman as $B$ and therefore is able to finish a job in $60\, days$ less than $B.$ Working together,they can do it in (in $days$)

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

$10$ men and $15$ women together can complete a work in $6$ days. It takes $100$ days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

$10$ men can cut $15$ trees in $2$ hours. If $2$ men leave the job,how many trees will be cut in $3$ hours?

$S, T$ and $U$ can complete a work in $40, 48$ and $60$ days respectively. They received $Rs. 10800$ to complete the work. They begin the work together,but $T$ left $2$ days before the completion of the work and $U$ left $5$ days before the completion of the work. $S$ completed the remaining work alone. What is the share of $S$ (in $Rs.$) from the total money?

$A$ and $B$ can do a piece of work in $10$ days. $B$ and $C$ can do it in $12$ days. $A$ and $C$ can do it in $15$ days. How long will $A$ take to do it alone? (in days)