$5$ 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)

$A$ can do a piece of work in $4 \, days$ and $B$ can do it in $12 \, days.$ In how many $days$ will they finish the work,both working together?

$A$ track of $100\, m$ can be built by $7\, men$ or $10\, women$ in $70\, days.$ How many days will $14\, men$ and $20\, women$ take to build a track of $600\, m$?

$A$ and $B$ can complete a piece of work in $12$ and $18 \text{ days}$ respectively. $A$ begins to do the work and they work alternatively one at a time for $1 \text{ day}$ each. The whole work will be completed in (in $\text{days}$):

$A, B$,and $C$ are employed to do a piece of work for $Rs. 529$. $A$ and $B$ together are supposed to do $\frac{19}{23}$ of the work,and $B$ and $C$ together are supposed to do $\frac{8}{23}$ of the work. What amount should $A$ be paid? (in $Rs.$)

$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?