The average of $6$ observations is $12$. $A$ new seventh observation is included and the new average is decreased by $1$. The seventh observation is

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

$A$ librarian purchased $50$ storybooks for his library. He realized that he could get $14$ more books by spending $Rs. 76$ more,and the average price per book would be reduced by $Rs. 1$. What was the average price (in $Rs.$) of each book he initially bought?

The average weight of $A, B$ and $C$ is $84 \, kg$. If $D$ joins,the average weight now is $80 \, kg$. If another person $E$,who is $3 \, kg$ heavier than $D$,replaces $A$,then the average weight of $B, C, D$ and $E$ becomes $79 \, kg$. What is the weight of $A$ in $kg$?

What is the average of the squares of the first $19$ natural numbers?

Out of $30$ teachers of a school,a teacher of age $60$ $years$ retired. In his place another teacher of age $30$ $years$ was appointed. As a result,the mean age of the teachers will