$A$ and $B$ working separately can do a piece of work in $10 \text{ days}$ and $15 \text{ days}$ respectively. If they work on alternate days beginning with $A$,in how many days will the work be completed?

$P$ 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?

$A, B$ and $C$ 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. What is the time taken to finish the remaining work? (in days)

$A$ contract is to be completed in $50 \text{ days}$ and $105 \text{ men}$ were set to work,each working $8 \text{ hours a day}$. After $25 \text{ days}$,$\frac{2}{5}$ of the work is finished. How many additional men must be employed so that the work may be completed on time,with each man now working $9 \text{ hours a day}$?

If $6$ men and $8$ boys can do a piece of work in $10$ days and $26$ men and $48$ boys can do the same work in $2$ days,the time taken by $15$ men and $20$ boys to do the same type of work will be (in days)

$8$ children and $12$ men complete a certain piece of work in $9$ days. If each child takes twice the time taken by a man to finish the work,in how many days will $12$ men finish the same work?