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 of marks obtained by $100$ candidates in a certain examination is $30$. If the average marks of passed candidates is $35$ and that of the failed candidates is $10$,what is the number of candidates who passed the examination?

The average age of a board of directors of a company,having $10$ directors,was $48$ years. Coincidentally,when a director aged $53$ resigned from the board,another director died on the same day. $A$ new director aged $34$ joined the board. Next year in the same month,the average age of all the $9$ directors was found to be $46$ years. The age of the late (i.e.,dead) director at the time of his death was (in years):

The average age of three boys is $15$ years. If the ratio of their ages is $3:5:7$,what is the age of the oldest boy in years?

The average of $6$ numbers is $8$. What is the $7^{th}$ number so that the average becomes $10$?

$A$ club has $15$ men and $25$ women. The average age of men is $10 \text{ years}$ and the average age of women is $12 \text{ years}$. What is the average age of the whole club in years?