$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is:

$5$ 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)

If $A$ works alone,he would take $4$ days more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone,he would take $16$ days more to complete the job than if $A$ and $B$ work together. How many days would they take to complete the work if both of them worked together?

Nikita,Nishita,and Kavita can complete a work in $2 \frac{2}{3}$ days. If Nishita and Kavita can complete it in $4$ days,and Nishita alone can do it in $6$ days,then in how many days can Nikita and Nishita complete the work?

$A$ does half as much work as $B$ in $\frac{3}{4}$ of the time. If together they take $18$ days to complete a work,then how much time shall $B$ take to complete it? (in days)

$A$ 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 $Rs.$)