$4$ men and $6$ women can complete a work in $8$ days,while $3$ men and $7$ women can complete it in $10$ days. In how many days will $10$ women complete it?

Ram and Hari can cut $12 \, kg$ of nuts in $2 \, days$. After $5 \, days$, Hari left the work. Ram took $8$ more days to cut the rest of the nuts. If a total of $58 \, kg$ of nuts were cut, the time taken by Hari to cut $10 \, kg$ of nuts is (in days):

$A$ can do a piece of work in $30 \text{ days}$ while $B$ can do it in $40 \text{ days}$. $A$ and $B$ working together can do it in (in $\text{days}$)

$P$ and $Q$ can do a piece of work in $30$ and $40$ days respectively. They began the work together,but $P$ left after some days and $Q$ finished the remaining work in $12$ days. After how many days did $P$ leave?

Ram can finish a work in $15 \text{ days}$ working $8 \text{ hrs/day}$. Fari can finish it in $6 \frac{2}{3} \text{ days}$ at $9 \text{ hrs/day}$. Find in how many days both can finish it together,if both work $10 \text{ hrs/day}$?

$5$ men can prepare $10$ toys in $6$ days working $6$ hours a day. Then,in how many days can $12$ men prepare $16$ toys working $8$ hours a day? (in days)