$A$ piece of work was to be completed in $40$ days. $A$ number of men employed upon it did only half the work in $24$ days. $16$ more men were then set on,and the work was completed in the specified time. How many men were employed at first?

$10$ men can cut $15$ trees in $2$ hours. If $2$ men leave the job,how many trees will be cut in $3$ hours?

$A$ alone can complete a work in $16$ days and $B$ alone in $12$ days. Starting with $A$,they work on alternate days. The total work will be completed in (in days):

$4$ men and $6$ women can complete a work in $8$ days,while $3$ men and $7$ women can complete it in $10$ days. In how many days will $10$ women complete it?

$A$ 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):

The total number of men,women,and children working in a factory is $18$. They earn $Rs. 4000$ in a day. If the sum of the wages of all men,all women,and all children is in the ratio $18: 10: 12$,and the wages of an individual man,woman,and child are in the ratio $6: 5: 3$,then how much does a woman earn in a day? (in $Rs.$)