$4$ men and $6$ women together can complete a work in $8$ days,while $3$ men and $7$ women together can complete it in $10$ days. How many days will $20$ women working together take to complete the same work?

$A$ can complete a piece of work in $10$ days,while $B$ alone can complete it in $15$ days. They work together for $5$ days and the rest of the work is done by $C$ in $2$ days. If they receive $Rs. 450$ for the whole work,how should they divide the money? (in $Rs.$)

$12$ men complete a work in $9$ days. After they have worked for $6$ days,$6$ more men join them. How many days will they take to complete the remaining work?

$A,$ $B,$ 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?

$A$ can complete a work in $m$ days and $B$ can complete it in $n$ days. How many days will it take to complete the work if both $A$ and $B$ work together?

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 $\text{hours}$)