$A$ can do a work in $20 \, days$ and $B$ in $40 \, days$. If they work on it together for $5 \, days$,then the fraction of the work that is left is:

$A$ track of $100\, m$ can be built by $7\, men$ or $10\, women$ in $70\, days.$ How many days will $14\, men$ and $20\, women$ take to build a track of $600\, m$?

$3$ 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 $Rs.$)

$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is:

$7$ men can complete a piece of work in $12$ days. How many additional men will be required to complete double the work in $8$ days?

$P$ can do $\left(\frac{1}{4}\right)$ of the work in $10$ days. $Q$ can do $40\%$ of the work in $40$ days and $R$ can do $\left(\frac{1}{3}\right)$ of the work in $13$ days. Who will complete the work first?