The average weight of $24$ students in section $A$ of a class is $58 \,kg,$ whereas the average weight of $26$ students in section $B$ of the same class is $60.5 \,kg$. Find out the average weight of all the $50$ students of the class. (in $kg$)

Three years ago,the average age of a family of $5$ members was $27 \, \text{years}$. The present average age is also $27 \, \text{years}$ after the inclusion of a child into the family. Find the age of the child in years.

Mr. Patel walked $6 \, km$ to reach the station from his house,then he boarded a train whose average speed was $60 \, km/hr$ and thus he reached his destination. In this way,he took a total of $3 \, hours$. If the average speed of the entire journey was $32 \, km/hr$,then the average speed of walking is (in $km/hr$):

The average of $8$ numbers is $20$. The average of the first two numbers is $15 \frac{1}{2}$ and that of the next three is $21 \frac{1}{3}$. If the sixth number is less than the seventh and eighth numbers by $4$ and $7$ respectively,then the eighth number is:

The average salary per head of all the workers in a company is $Rs. \,95$. The average salary of $15$ officers is $Rs. \,525$ and the average salary per head of the rest is $Rs. \,85$. Find the total number of workers in the workshop.

$A$ 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?