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 $Rs$.

The average of the first $25$ numbers is $10$ and the average of the next $25$ numbers is $12$. The average of all $50$ numbers is:

The average of $13$ results is $60$. If the average of the first $7$ results is $59$ and that of the last $7$ results is $61$,what will be the seventh result?

$A$ professional institute's total expenditure on students for a particular course is partly fixed and partly varies linearly with the number of students. The average expense per student is $Rs.\,615$ when there are $24$ students and $Rs.\,465$ when there are $40$ students. What is the average expense when there are $60$ students? (in $Rs.$)

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 $b > c$)

In a $20$ over match,the required run rate to win is $7.2$. If the run rate is $6$ at the end of the $15^{th}$ over,the required run rate to win the match is