$A$ library has an average of $510$ visitors on Sundays and $240$ on other days. The average number of visitors per day in a month of $30$ days beginning with a Sunday is:

The average of $3$ numbers is $22$. If the first number is $\frac{3}{8}$ of the sum of the other two numbers,what is the first number?

The average marks of students in an examination was $65$. It was later found that the marks of one student had been wrongly entered as $83$ instead of $38$. If there were $50$ students, what is the correct average?

The average of $25$ results is $20$. The average of the first $12$ results is $15$ and that of the last $12$ results is $18$. Then,the $13^{th}$ result is:

$A$ person covers $9 \, km$ with a speed of $3 \, km/h$,$25 \, km$ with a speed of $5 \, km/h$,and $30 \, km$ with a speed of $10 \, km/h$. Find the average speed of the person in $km/h$.

$A, B, C, D,$ and $E$ are five consecutive even numbers. The average of $A$ and $E$ is $46$. What is the largest number?