If $10$ men or $18$ boys can do a work in $15$ days,then the number of days required by $15$ men and $33$ boys to do twice the work is

Hemant decided to build a farmhouse in $40$ days. He employed $100$ men in the beginning and $100$ more after $35$ days and completed the construction in the stipulated time. If he had not employed the additional men,how many days behind schedule would it have been finished? (in days)

$A$ $10\, \text{hectare}$ field is reaped by $2\, \text{men},$ $3\, \text{women},$ and $4\, \text{children}$ together in $10\, \text{days}.$ If the working capabilities of a man, a woman, and a child are in the ratio $5: 4: 2,$ then a $16\, \text{hectare}$ field will be reaped by $6\, \text{men},$ $4\, \text{women},$ and $7\, \text{children}$ in how many days?

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

$3$ women and $18$ children together take $2$ days to complete a piece of work. How many days will $9$ children alone take to complete the piece of work,if $6$ women alone can complete the piece of work in $3$ days?

$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?