The average of $13$ results is $50$. If the average of the first $7$ results is $52$ and that of the last $7$ results is $49$,find the $7^{th}$ result.

The average temperature of Monday,Tuesday,Wednesday and Thursday is $60^{\circ}$. The average temperature for Tuesday,Wednesday,Thursday and Friday is $63^{\circ}$. If the ratio of temperature for Monday and Friday is $21: 25,$ then what is the temperature of Friday? (in $^{\circ}$)

Find the average of all prime numbers between $60$ and $90$.

Amitabh's average expenditure from $January$ to $June$ is $Rs. 4200$. He spends $Rs. 1200$ in $January$ and $Rs. 1500$ in $July$. What is the average expenditure for the months of $February$ to $July$ (in $Rs.$)?

$A$ 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 $Rs.$)

The average of three consecutive odd numbers is $52$ more than $\frac{1}{3}$ of the largest of these numbers. What is the smallest of these numbers?