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

The average weight of $45$ students in a class is $52 \, kg.$ Five of them whose average weight is $48 \, kg$ leave the class and other $5$ students whose average weight is $54 \, kg$ join the class. What is the new average weight (in $kg$) of the class?

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

$10$ years ago,the average age of a family of $4$ members was $24$ years. Two children have been born (with an age difference of $2$ years),and the present average age of the family remains the same. The present age of the youngest child is (in years):

There are $6$ consecutive odd numbers in increasing order. The difference between the average of the squares of the first $4$ numbers and the last $4$ numbers is $64$. If the sum of the squares of the first and the last element is $178$,then the average of all the $6$ numbers is:

The average revenue of $13$ consecutive years of a company is $Rs. 70$ lakhs. If the average of the first $7$ years is $Rs. 65$ lakhs and that of the last $7$ years is $Rs. 77$ lakhs,find the revenue for the $7^{th}$ year (in $Rs.$ lakhs).