Working efficiencies of $A$ and $B$ for completing a piece of work are in the ratio $3: 4$. The number of days taken by them to complete the work will be in the ratio:

$A$ 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?

$A$ certain sum of money is sufficient to pay wages for $21$ days of $X$ or $28$ days of $Y$. The money is sufficient to pay the wages of both for ........ 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?

While working $7$ hours a day,$A$ alone can complete a piece of work in $6$ days and $B$ alone in $8$ days. In what time would they complete it together,working $8$ hours a day? (in days)

$A$ and $B$ can complete a piece of work in $12$ and $18 \text{ days}$ respectively. $A$ begins to do the work and they work alternatively one at a time for $1 \text{ day}$ each. The whole work will be completed in (in $\text{days}$):