$A$ and $B$ can do a work in $12$ days,$B$ and $C$ in $15$ days,and $C$ and $A$ in $20$ days. If $A, B,$ and $C$ work together,they will complete the work in (in days):

$A$ man,a woman,and a boy can complete a job in $3, 4,$ and $12$ days respectively. How many boys must assist $1$ man and $1$ woman to complete the job in $\frac{1}{4}$ of a day?

$P$ can do $\left(\frac{1}{4}\right)$ of the work in $10$ days. $Q$ can do $40\%$ of the work in $40$ days and $R$ can do $\left(\frac{1}{3}\right)$ of the work in $13$ days. Who will complete the work first?

$A$ can finish a work in $18$ days and $B$ can do the same work in half the time taken by $A$. Then,working together,what part of the same work can they finish in a day?

Four examiners can examine a certain number of answer papers in $10 \, \text{days}$ by working for $5 \, \text{hours}$ a $\text{day}$. For how many $\text{hours}$ in a $\text{day}$ would $2$ examiners have to work in order to examine twice the number of answer papers in $20 \, \text{days}$? (in $\text{hours}$)

If a work can be completed by $A$ in $30 \text{ days}$ and by $B$ in $60 \text{ days}$,then the number of days taken by them to finish the work,working together,is