$A$ works thrice as good as $B$ and is,therefore,able to finish a piece of work in $60 \text{ days}$ less than $B$. Find the time in which they can complete it,working together (in $\text{days}$).

$A$ piece of work can be completed by $10$ men and $6$ women in $18$ days. Men work $9$ hours per day while women work $7.5$ hours per day. The per hour efficiency of a woman is $\frac{2}{3}$ of a man's efficiency. In how many days will $10$ men and $9$ women complete the work?

$A$ can do a piece of work in $8$ days. $A$ undertook it for $Rs. 320$. With the help of $B$,he finishes the work in $6$ days. $B$'s share is (in $Rs.$):

$A$ and $B$ undertake a piece of work for $Rs. 250$. $A$ alone can do that work in $5$ days and $B$ alone can do that work in $15$ days. With the help of $C$,they finish the work in $3$ days. If everyone gets paid in proportion to the work done by them,the amount $C$ will get is (in $Rs.$)

$5$ men can complete a work in $2$ days,$4$ women can complete the same work in $3$ days and $5$ children can do it in $3$ days. $1$ man,$1$ woman and $1$ child,working together,can complete the work in (in days):

$A$ and $B$ can do a work in $12$ days,$B$ and $C$ in $15$ days,and $C$ and $A$ in $20$ days. If $A, B,$ and $C$ work together,they will complete the work in (in days):