$A, B$ and $C$ individually can do a work in $10\, days, 12\, days$ and $15\, days,$ respectively. The number of days required to finish the work by $A, B$ and $C$ working together is? (in $days$)

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)

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):

$A$ can finish a work in $24$ days,$B$ in $9$ days,and $C$ in $12$ days. $B$ and $C$ start the work but are forced to leave after $3$ days. The remaining work was done by $A$ in (in days):

$A$ and $B$ can do a job together in $7$ days. $A$ is $1\frac{3}{4}$ times as efficient as $B$. The same job can be done by $A$ alone in (in days):

$P$ 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