$A$ 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.

$A$ does half as much work as $B$ in $\frac{3}{4}$ of the time. If together they take $18$ days to complete a work,then how much time shall $B$ take to complete it? (in days)

$2$ men and $4$ boys can do a piece of work in $10$ days,while $4$ men and $5$ boys can do it in $6$ days. Men and boys are paid wages according to their output. If the daily wage of a man is $Rs. 40$,then the ratio of daily wages of a man and a boy will be

Twenty women can do a work in $16$ days. Sixteen men can complete the same work in $15$ days. What is the ratio between the capacity of a man and a woman?

$A$ can finish a work in $24$ days,$B$ in $9$ days and $C$ in $12$ days. $B$ and $C$ start the work but are forced to leave after $3$ days. The remaining work was done by $A$ in (in days):

$A, B$ and $C$ individually can do a work in $10\, days, 12\, days$ and $15\, days,$ respectively. The number of days required to finish the work by $A, B$ and $C$ working together is? (in $days$)