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 diminishes by $Rs. 1$. Find the actual expenditure of the mess (in $Rs.$).

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 average temperature of the first $4 \, \text{days}$ of a week is $38.6^{\circ} \text{C}$ and that of the last $4 \, \text{days}$ is $40.3^{\circ} \text{C}$. If the average temperature of the entire week is $39.1^{\circ} \text{C}$, find the temperature on the $4^{th} \, \text{day}$ (in $^{\circ} \text{C}$).

The average of $10$ numbers is $7$. What will be the new average if each of the numbers is multiplied by $8$?

The average of the first $7$ integers in a series of $13$ consecutive odd integers is $37$. What is the average of the entire series?

If the average of the ages of Rakesh and Mohan is $15$,the average of the ages of Mohan and Ramesh is $12$,and the average of the ages of Rakesh and Ramesh is $13$,then what is the age of Mohan?