$40$ men can complete a work in $40$ days. They started the work together. But at the end of each $10^{th}$ day,$5$ men left the job. The work would have been completed in (in days):

$4$ men and $6$ women earn $Rs. \, 1600$ by doing a piece of work in $5$ days. $3$ men and $7$ women earn $Rs. \, 1740$ by doing the same work in $6$ days. In how many days can $7$ men and $6$ women complete the same work while earning $Rs. \, 3760$?

$2$ men and $4$ boys can do a piece of work in $10$ days,while $4$ men and $5$ boys can do it in $6$ days. Men and boys are paid wages according to their output. If the daily wage of a man is $Rs. 40$,then the ratio of daily wages of a man and a boy will be

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ in $40 \text{ days}$,while $C$ and $A$ in $60 \text{ days}$. $A, B, C$ together can complete the work in (in $\text{days}$):

$A$ and $B$ working separately can do a piece of work in $9$ and $12$ days,respectively. If they work for a day alternatively with $A$ beginning,the work would be completed in (in days):

$A$ work can be completed by $P$ and $Q$ in $12$ days,$Q$ and $R$ in $15$ days,and $R$ and $P$ in $20$ days. In how many days can $P$ alone finish the work?