$A$ batsman makes a score of $270$ runs in the $87^{th}$ inning and thus increases his average by a certain number of runs that is a whole number. Find the possible values of the new average.

The average of $8$ numbers is $20$. The average of the first two numbers is $15 \frac{1}{2}$ and that of the next three is $21 \frac{1}{3}$. If the sixth number is less than the seventh and eighth numbers by $4$ and $7$ respectively,then the eighth number is:

The sum of eight consecutive numbers of Set $A$ is $376$. What is the sum of $5$ consecutive numbers of another set if its minimum number is $15$ ahead of the average of Set $A$?

The average weight of $3$ men $A, B,$ and $C$ is $84 \, kg$. Another man $D$ joins the group and the average weight now becomes $80 \, kg$. If another man $E$,whose weight is $3 \, kg$ more than that of $D$,replaces $A$,then the average weight of $B, C, D,$ and $E$ becomes $79 \, kg$. The weight of $A$ in $kg$ is:

The average of three numbers,of which the greatest is $16$,is $12$. If the smallest is half of the greatest,what is the remaining number?

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day while the average expenditure per head decreases by $Rs. 1$. Find the original expenditure of the mess in $Rs$.