The average age of $20$ boys in the class is $15.6$ years. Five new boys join and the new average becomes $15.56$ years. What is the average age of the five new boys (in years)?

$16$ children are to be divided into two groups $A$ and $B$ of $10$ and $6$ children. The average percent marks obtained by the children of group $A$ is $75$ and the average percent marks of all the $16$ children is $76$. What is the average percent marks of children of group $B$?

The average weight of $36$ students is $50 \,kg$. It was found later that the figure of $37 \,kg$ was misread as $73 \,kg$. What is the correct average? (in $kg$)

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day while the average expenditure per head decreases by $Rs. 1$. Find the original expenditure of the mess in $Rs$.

$10 \, kg$ of rice priced at $Rs. \, 12$ per $kg$ is mixed with $6 \, kg$ of rice priced at $Rs. \, 16$ per $kg$. Find the average price in $Rs.$ per $kg$ of the whole mixture?

$A$ man travels by a car to his office at $60 \, km/h$ and returns home along the same route at $20 \, km/h$. Find the average speed of his whole journey (in $km/h$).