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:

There was one mess for $30$ boarders in a certain hostel. On the number of boarders being increased by $10,$ the expenses of the mess were increased by $Rs.\, 40$ per month while the average expenditure per head diminished by $Rs.\, 2.$ Find out the actual monthly expenses (in $Rs.$).

The average marks of $40$ students in an English exam is $72$. Later,it is found that three marks $64, 62,$ and $84$ were wrongly entered as $68, 65,$ and $73$. The average after the mistakes were rectified is:

The average of $30$ numbers is $12$. The average of the first $20$ of them is $11$ and that of the next $9$ is $10$. The last number is:

The average age of $6$ members of a family is $20$ years. If the age of a servant is included,the average age increases by $25\%$. What is the age (in years) of the servant?

The average of the first $46$ natural numbers is: