$P$ can complete $\frac{1}{4}$ of a work in $10$ days,$Q$ can complete $40\%$ of the same work in $15$ days,$R$ can complete $\frac{1}{3}$ of the work in $13$ days,and $S$ can complete $\frac{1}{6}$ of the work in $7$ days. Who will be able to complete the work first?

$A$ does half as much work as $B$ in $three-fourths$ of the time. If together they take $18$ days to complete a work,how much time shall $B$ take to do it alone? (in days)

$A,$ $B,$ and $C$ have to type $506$ pages to finish an assignment. $A$ can type a page in $12$ minutes,$B$ in $15$ minutes,and $C$ in $24$ minutes. If they divide the task into three parts so that all three of them spend an equal amount of time typing,what is the number of pages that $B$ should type?

$A$ takes twice as much time as $B$ or thrice as much time as $C$ to finish a piece of work. Working together,they can finish the work in $2$ days. $B$ can do the work alone in (in days):

Ramesh takes twice as much time as Mahesh and thrice as much time as Suresh to complete a job. If working together,they can complete the job in $4 \, \text{days}$,then the time taken by each of them separately to complete the work is (in $\text{days}$)

$A$ can do a piece of work in $120$ days and $B$ can do it in $150$ days. They work together for $20$ days. Then $B$ leaves and $A$ alone continues the work. After $12$ days,$C$ joins $A$ and the work is completed in $48$ days more. In how many days can $C$ do it if he works alone?