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)

$A$ certain number of men complete a work in $160\, days$. If there were $38\, men$ more, the work could be finished in $20\, days$ less. How many men were originally there?

$P$ and $Q$ complete a certain work in $30 \, days$,$Q$ and $R$ in $40 \, days$,while $R$ and $P$ in $60 \, days$. How long will they take to finish it together? (in $days$)

$3$ women and $18$ children together take $2$ days to complete a piece of work. How many days will $9$ children alone take to complete the piece of work,if $6$ women alone can complete the piece of work in $3$ days?

$P$ and $Q$ together can do a job in $6$ days. $Q$ and $R$ can finish the same job in $60/7$ days. $P$ started the work and worked for $3$ days. $Q$ and $R$ continued for $6$ days. Then the difference of days in which $R$ and $P$ can complete the job is

Ramesh takes twice as much time as Mahesh and thrice as much time as Suresh to complete a job. If working together,they can complete the job in $4 \, \text{days}$,then the time taken by each of them separately to complete the work is (in $\text{days}$)