The average of $9$ numbers is $30$. The average of the first $5$ numbers is $25$ and that of the last $3$ numbers is $35$. What is the $6^{\text{th}}$ number?

Total sum of all $9$ numbers = $9\times 30=270$.
Sum of the first $5$ numbers = $5\times 25=125$.
Sum of the last $3$ numbers = $3\times 35=105$.

Sum of these $8$ numbers ($5+3=8$) = $125+105=230$.

Therefore, the $6^{\text{th}}$ number = Total sum of $9$ numbers - Sum of $8$ numbers

$$6^{\text{th}}\text{ number}=270-230=40$$