$4$ 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. $20$ women working together will complete it in (in days):

Kim can do a work in $3 \, \text{days}$ while David can do the same work in $2 \, \text{days}$. Both of them finish the work together and get $Rs. 150$. What is the share of Kim? (in $Rs.$)

$A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They began to do the work together,but $A$ leaves after some days and then $B$ completed the remaining work in $23$ days. The number of days after which $A$ left the work was:

$A$ certain number of men complete a work in $160\, days$. If there were $38\, men$ more, the work could be finished in $20\, days$ less. How many men were originally there?

$A, B$ and $C$ together earn $Rs. 2700$ in $18$ days. $A$ and $C$ together earn $Rs. 940$ in $10$ days. $B$ and $C$ together earn $Rs. 1520$ in $20$ days. Find the daily earning of $C$ (in $Rs.$).

$8$ men can complete a piece of work in $20$ days. $8$ women can complete the same work in $32$ days. In how many days will $5$ men and $8$ women together complete the same work?