The average marks of a class of $35$ children is $35$. The marks of one of the students,who got $35$,was incorrectly entered as $65$. What is the correct average of the class?

In a class,the average height of all students is $a \text{ cm}$. Among them,the average height of $10$ students is $b \text{ cm}$ and the average height of the remaining students is $c \text{ cm}$. Find the number of students in the class. (Here $a > c$ and $b > c$)

The average weight of $8$ sailors in a boat is increased by $1 \, kg$ if one of them weighing $56 \, kg$ is replaced by a new sailor. The weight of the new sailor is (in $kg$):

The average age of $80$ boys in a class is $15.$ The average age of a group of $15$ boys in the class is $16$ and the average age of another $25$ boys in the class is $14.$ What is the average age of the remaining boys in the class?

The average weight of $A, B$ and $C$ is $84 \, kg$. If $D$ joins,the average weight now is $80 \, kg$. If another person $E$,who is $3 \, kg$ heavier than $D$,replaces $A$,then the average weight of $B, C, D$ and $E$ becomes $79 \, kg$. What is the weight of $A$ in $kg$?

Out of nine persons,eight persons spent $Rs. \,30$ each for their meals. The ninth person spent $Rs. \,20$ more than the average expenditure of all the nine persons. What was the total money spent by all of them (in $Rs.$)?