$10$ women can complete a work in $7$ days and $10$ children take $14$ days to complete the work. How many days will $5$ women and $10$ children take to complete the work?

$A$ completes a piece of work in $4 \text{ days}$ and $B$ completes it in $6 \text{ days}$. If they both work on it together,then the number of days required to complete the same work is (in $\text{days}$):

$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

$A$'s $2$ days work is equal to $B$'s $3$ days work. If $A$ can complete the work in $8$ days,then to complete the work $B$ will take (in days):

$A$ contract is to be completed in $92$ days and $234$ men were set to work,each working $16$ hours a day. After $66$ days,$\frac{4}{7}$ of the work is completed. How many additional men may be employed,so that the work may be completed in time,each man now working $18$ hours a day?

$A, B$ and $C$ can do a piece of work in $20, 30$ and $60$ days respectively. In how many days can $A$ do the work if he is assisted by $B$ and $C$ on every third day?