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)

$A$ group of men decided to do a work in $10 \, days,$ but five of them absented themselves. If the rest of the group finished the work in $12 \, days,$ find the original number of men? (in $men$)

$A$ 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?

$A$ can do a certain work in $12$ days. $B$ is $60\%$ more efficient than $A$. How many days will $B$ and $A$ together take to do the same job?

Ram and Hari can cut $12 \, kg$ of nuts in $2 \, days$. After $5 \, days$, Hari left the work. Ram took $8$ more days to cut the rest of the nuts. If a total of $58 \, kg$ of nuts were cut, the time taken by Hari to cut $10 \, kg$ of nuts is (in days):

$45$ men can complete a work in $16$ days. Four days after they started working,$36$ more men joined them. How many days will they now take to complete the remaining work?