$A$ man,a woman,and a boy can complete a job in $3, 4,$ and $12$ days respectively. How many boys must assist $1$ man and $1$ woman to complete the job in $\frac{1}{4}$ of a day?

Working $7\, \text{hours}$ daily,$24$ men can complete a piece of work in $27$ $\text{days}$. In how many $\text{days}$ would $14$ men complete the same piece of work working $9\, \text{hours}$ daily?

$3$ men and $4$ boys can complete a certain work in $8$ days,while $4$ men and $4$ boys can complete the same work in $6$ days. Then $2$ men and $4$ boys will finish it in ........ days.

$3$ persons undertake to complete a piece of work for $Rs. 1,200$. The $first$ person can complete the work in $8$ days,the $second$ person in $12$ days,and the $third$ person in $16$ days. They complete the work with the help of a $fourth$ person in $3$ days. What does the $fourth$ person get? (in $Rs.$)

$A$ and $B$ can complete a piece of work in $45$ and $40$ days,respectively. They began the work together,but $A$ leaves after some days and $B$ completed the remaining work in $23$ days. After how many days did $A$ leave?

$10$ men can complete a piece of work in $15$ days and $15$ women can complete the same work in $12$ days. If all the $10$ men and $15$ women work together,in how many days will the work be completed?