$A$ and $B$ can do a piece of work in $20$ days and $12$ days respectively. $A$ started the work alone and then after $4$ days $B$ joined him until the completion of the work. How long did the work last? (in days)

$P$,$Q$ and $R$ contracted to do a work for $Rs. 4200$. $P$ can do the work in $6$ days,$Q$ in $10$ days and $R$ in $12$ days. If they work together to do the work,what is the share of $R$ (in $Rs.$)?

$A$ contractor undertakes to dig a canal $12 \, km$ long in $350 \, days$ and employs $45$ men. After $200 \, days$ he finds that only $4.5 \, km$ of the canal has been completed. Find the number of extra men he must employ to finish the work in time (in $men$).

There is sufficient food for $400$ men for $31$ days. After $28$ days,$280$ men leave the place. For how many days will the rest of the food last for the rest of the men? (in days)

$3$ 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:

$A$ can do a piece of work in $16$ days and $B$ in $24$ days. They take the help of $C$ and all three together finish the work in $6$ days. If the total remuneration for the work is $Rs. 400$,what is the amount (in $Rs.$) each will receive in proportion to the work done?