$A$ and $B$ can do a job together in $7$ days. $A$ is $1\frac{3}{4}$ times as efficient as $B$. The same job can be done by $A$ alone in (in days):

$A$ can finish a work in $18$ days and $B$ can do the same work in half the time taken by $A$. Then,working together,what part of the same work can they finish in a day?

$10$ men can finish a piece of work in $10$ days,whereas it takes $12$ women to finish it in $10$ days. If $15$ men and $6$ women undertake to complete the work,how many days will they take to complete it?

$A$ and $B$ can do a work in $45 \text{ days}$ and $40 \text{ days}$,respectively. They began the work together,but $A$ left after some time and $B$ completed the remaining work in $23 \text{ days}$. After how many days of the start of the work did $A$ leave?

$6$ men or $12$ women can do a piece of work in $20$ days. In how many days can $8$ men and $16$ women do twice as big as this work?

If a job is to be completed in $10 \, \text{days}$,it requires $270 \, \text{persons}$. If $180 \, \text{persons}$ take up the same job,they will finish it in (in $\text{days}$):