The mean of $11$ numbers is $35$. If the mean of the first $6$ numbers is $32$ and that of the last $6$ numbers is $37$, then find the sixth number.

The average age of a group of $15$ students is $10 \, \text{years}$. When $5$ more students joined the group,the average age increased by $1 \, \text{year}$. If the average age of the $5$ new students is $x$,find the value of $x$ (in $\text{years}$).

The average age of $15$ students in a class is $15 \text{ years}$. Out of these,the average age of $5$ students is $14 \text{ years}$ and that of the other $9$ students is $16 \text{ years}$. What is the age of the $15^{th}$ student? (in $\text{years}$)

The average weight of $3$ men $A, B,$ and $C$ is $84 \, kg$. Another man $D$ joins the group and the average weight now becomes $80 \, kg$. If another man $E$,whose weight is $3 \, kg$ more than that of $D$,replaces $A$,then the average weight of $B, C, D,$ and $E$ becomes $79 \, kg$. The weight of $A$ in $kg$ is:

The sum of five numbers is $260$. The average of the first two numbers is $30$ and the average of the last two numbers is $70$. What is the third number?

The average of $X_{1}, X_{2}$ and $X_{3}$ is $14$. Twice the sum of $X_{2}$ and $X_{3}$ is $30$. What is the value of $X_{1}$?