$A$ does a work in $10$ $days$ and $B$ does the same work in $15$ $days$. In how many $days$ will they together do the same work?

$A$ and $B,$ working separately,can complete a piece of work in $9$ and $12$ days,respectively. If they work for a day alternately,$A$ beginning,in how many days will the work be completed?

$10$ men working $6\, \text{h}$ a day can complete a work in $18\, \text{days}$. How many $\text{hours per day}$ must $15$ men work to complete the same work in $12\, \text{days}$?

$2$ 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?

$5$ men or $7$ women can earn $Rs. 5,250$ per day. How much would $7$ men and $13$ women earn per day? (in $Rs.$)

$P$ can do a piece of work in $9$ days. $Q$ is $50\%$ more efficient than $P$. The number of days it takes for $Q$ to do the same piece of work is